
■ ■ 







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LIBRARY OF CONGRESS, 



Sheli/'.AAk 

UNITED STATES OF AMERICA. 




C^vfe-*?* 




LABORATORY EXERCISES 



ELEMENTARY PHYSICS 



CHARLES R. ALLEN, S.B. 

Instructor in the New Bedford, Mass., High School 




MAR 18 182? ) 

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NEW YORK 
HENRY HOLT AND COMPANY 

1892 



Copyright, 1892, 

BY 

HENRY HOLT & CO. 



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s\ Z-. Robert Drummond, 

Electrotyper and Printer, 
New York. 



PREFACE. 



Most of the experiments in this collection exact of the 
pupil measurements of some sort, that is, are quantitive. 
A few, included for the training in accurate work they 
afford or for their suggestiveness, demand the investigations 
of the conditions under which certain phenomena develop. 
They require, however, the use of some physical instrument. 
Those purely illustrative are given because they demand 
more careful observation than the pupil can give to a lec- 
ture experiment. In the course will be found, I think, 
illustrations of many of the 'more common methods of 
physical research. The exercises are planned for young 
pupils with no previous training in physics, employ no un- 
duly expensive apparatus, and require no more than forty- 
five minutes each in the laboratory. The subjects selected 
are among those bearing on the commoner applications of 
physical science. Pains have been taken to so frame the 
instructions that the pupil can prepare himself beforehand 
to make the most of his laboratory time with the least help 
from his instructor. This I regard of prime importance. 
Unless the instructor assures himself before each exercise 
that the pupils understand what they are to do and how to 
do it, they will pretty surely exceed the time-limit, and may 
even make wreck of the whole exercise. Five unprepared 
pupils require more attention than fifteen who have thor- 
oughly mastered the preliminary work. When entirely 
new or especially complicated apparatus is to be used, I 



IV PREFACE. 

find it advisable to place a " dummy" set before the class, 
and spend part or the whole of one period in requiring 
individual pupils to go through the motions with it, to 
answer questions on the general method and the special 
manipulations, and, in case of a complicated calculation, 
to work out results from imaginary data. 

The arrangement and even the phrasing of the ma- 
terial is the outgrowth of much searching for a general 
form which would be most effective in stimulating clear 
and independent thinking. Each exercise is introduced 
by some preliminary explanation and a distinct statement 
of its object. This puts before the pupil the precise thing 
he is after, and the general course of his investigation. 
The manipulation is then described with what some mav 
deem unnecessary minuteness, but I find this minuteness 
part of the secret of speed and success. I have added ques- 
tions where I have found them convenient in guiding the 
pupils' thought, but in no instance, I believe, do they con- 
tain their own answer. In a few cases I have given alter- 
native exercises on the same topic, for the purpose of 
suiting the varying experimental aptitude of pupils. 

In the order of subjects, the exercises form a somewhat 
roughly graded course, from magnetic phenomena, where 
work is simplest and most stimulative to attention, through 
experiments involving the measurement of a single value 
by means of some single instrument, to the more compli- 
cated quantitive determinations of Dynamics. This order 
places the most difficult part of Physics last, where the 
pupil can bring to his aid, in grasping abstract ideas and 
performing intricate experiments, the training acquired in 
the previous parts of the course. But since the instruc- 
tions in one subject do not assume a previous knowledge 
of any other, there is nothing to prevent the subjects being- 
taken up in any order desired, though of course practice 
in mensuration should precede the quantitive exercises. 



PREFACE. V 

The book is made up mainly of the author's instructions 
to his own pupils for their laboratory work. The course 
of which this forms a part includes also the performance 
of all necessary descriptive experiments before the class, 
and the use of a text-book. Before the pupil goes to work 
in the laboratory at all, he should be given a general idea 
of how knowledge is acquired experimentally, and the steps 
involved in carrying on an experimental investigation. 
The instruction on these points should be illustrated by 
some simple typical experiments by the teacher. After- 
wards the relative order of text-book and laboratory work 
will naturally depend upon the nature of the laboratory 
exercises. In exercises involving the study of conditions, 
as in those on Magnetism, and some of those on Electricity 
and Heat, the author prefers that the laboratory work pre- 
cede the text-book work; but in exercises involving definite 
measurement, as in Specific Gravity and Specific Heat, this 
order may well be reversed. Certainly, in the determina- 
tion of a physical law by measurements of two values, as in 
the exercises on Elasticity or on the Pendulum, the labora- 
tory work should come first. 

In order to reduce the volume to a convenient size for 
the laboratory table, all matter meant chiefly for the in- 
structor is appended to the Teachers' Edition and omitted 
from the Pupils' Edition, the two being identical in other 
respects. Appendix A offers general suggestions for ar- 
ranging the pupil's work and economizing his and the in- 
structor's time, together with directions for applying the 
ordinary 110-volt Edison electric current to laboratory 
work, and for the care of mercury. Appendix B gives 
complete lists of all the apparatus needed for each exercise, 
hints as to substitutes and duplicates, and itemized esti- 
mates of cost with references to dealers' catalogues. Ap- 
pendix C contains full instructions for making the more 
important pieces of apparatus. Appendix D furnishes 



VI PREFACE. 

topical references to Avery's "First Principles of Natural 
Philosophy" and "Elements of Natural Philosophy," to 
Gage's "Elements of Physics" and " Introduction to Physi- 
cal Science," and to Hall and Bergen's "Text-Book of 
Physics," supplemented by hints on conducting the vari- 
ous exercises, the educational purpose each is meant to 
serve, the degree of accuracy to be expected, etc. 

While, so far as I know, none of the experiments will be 
found elsewhere in exactly their form here, many have been 
modified from other manuals. No attempt is made to 
credit each exercise to the source of the original idea. The 
chief books laid under contribution are Worthington's 
"Laboratory's Practice," Stewart and Gee's "Physics," 
Pickering's "Physical Manipulations," the Harvard College 
Course of Experiments, and Maxwell's " Matter and Mo- 
tion." The metric system has been employed because it is 
the language of quantity in physical laboratories, scientific 
text-books and journals, and the higher scientific manu- 
facturing processes the world over. Pupils learn with such 
ease to use so much of it as this book requires, that it forms 
no bar to their progress. 

C. R. A. 

New Bedford, Mass., February 1, 1892. 



CONTENTS. 



MAGNETISM. 



Exercise 1. General Study of a Magnet, .... 
" 2. The Action of the Attracted Body on the Magnet, 
" 3. Mutual Action of two Magnets, 
" 4. Induced Magnetism. Breaking Magnets, 
" 5. Law of Induced Magnets, .... 

" 6. Lines of Magnetic Force, .... 



PAGE 
1 

4 



10 
12 



CURRENT ELECTRICITY. 



Exercise 1. Voltaic Electricity, .... 
" 2. Conditions for Producing Current, . 
" 3. Action of Currents on Magnets, 
" 4. Conditions Affecting Electrical Resistance 
" 5. Electrical Resistance, 

6. Methods of Connecting Galvanic Cells, 
" 7. Relative Resistance, .... 
" 8. A. Measurement of Resistance, 
B. Measurement of Resistance, 
" 9. Electro-motive Force, 
" 10. Electro-magnetism, .... 
" 11. Induced Currents, . . 



17 
20 
25 
29 
33 
36 
40 
42 
45 
48 
50 
52 



MENSURATION. 

Notes on Measurement, 56 

Determination of Length, 59 

Exercise 1. Practice in the Use of Linear Scales, . . .62 
" 2. The Relation of Circumference to Diameter, . . 64 

vii 



Vlll CONTENTS. 

PAGE 

Determination of Volumes, 67 

Exercise 3. Practice in Determining Volumes, . . . .74 

" 4. Cross-section and Internal Diameter of a Tube, . 76 

Determination of Weight, 78 

Exercise 5. Practice in Weighing, 83 

" 6. Estimation of Metric Values, 84 

Notes on Errors, 85 

Exercise 7. Physical and Chemical Change, . . . .86 



DENSITY AND SPECIFIC GRAVITY. 

Exercise 1. Density and its Determination, . . . .89 

" 2. Determination of Specific Gravity, . . . .92 
" 3. Weight Lost by a Body when Immersed in a Liquid, 93 
" 4. Specific Gravity by Immersion, . . . .96 
" 5. Liquid Pressure Due to Weight, . . . .99 
" 6. Specific Gravity of Liquids by Balancing, , . 103 
" 7. Weight of Liquid Displaced by a FloatiDg Body, . 106 
" 8. Atmospheric Pressure and the Barometer, . . 107 
" 9. Specific Gravity of Two Liquids by Balancing 

against Atmospheric Pressure, . . . .109 



HEAT. 

Introductory 112 

Exercise 1. How Heat Travels, 113 

" 2. Testing Thermometers 117 

" 3. Temperature and Physical Form, . . . .119 
" 4. Laws of Cooling, 124 

5. Melting and Boiling Points, 125 

6. Heat Capacity, 127 

" 7. Determination of Specific Heat, . . . .128 

8. Latent Heat, 133 

" 9. Coefficient of Linear Expansion, .... 138 
" 10. Cubical Coefficient of a Liquid, .... 145 
" 11. Coefficient of Expansion of a Gas at Constant Press- 
ure, 146 

" 12. Absorption and Radiation, 150 

" 13. Solution, 152 



CONTENTS. 



DYNAMICS. 

Exercise 1. Action of a Force upon a Body, .... 153 

2. The Force of Friction 156 

3. Composition of Forces, 160 

4. Parallel Forces, 166 

5. The Inclined Plane, 169 

6. The Wedge and the Screw, 173 

7. Laws of the Pendulum, 174 

8. Action and Reaction, 177 

9. The Force of Tenacity, 181 

10. The Force of Elasticity, 183 

11. Boyle's Law, 185 

12. Specific Gravity without Scales or Weights, . . 189 

LIGHT. 

Exercise 1. Foci of Lenses, 191 

" 2. Distance and Intensity of Light, .... 194 

3. Radiation of Light, 197 

" 4. Candle-power by the Rumford Photometer, . . 199 

SOUND. 

Exercise 1. Conditions Affecting Pitch, 201 

2. Velocity of Sound, 203 

APPENDICES. 

Appendix A. General Suggestions, 205 

" B. Lists of Apparatus, 213 

" C. Construction of Apparatus, 223 

" D. Notes and References, 255 



LABORATORY PHYSICS. 



MAGNETISM. 
EXERCISE 1. 

GENERAL STUDY OF A MAGNET. 

EXPERIMENT 1. 

Apparatus.— Bar magnet, a pieoe of steel (knife-blade or knitting- 
needle), some carpet-tacks; pieces of paper, glass, wood, etc.; cop 
per tacks; a piece of window-glass two or three inches square; iron- 
filings; larger tack or nail; bottle which may contain the iron-filings 
or block of wood. 

Object. — To compare the results of bringing first a piece 
of steel and then the magnet near a piece of iron or 
another piece of steel. 

Manipulation. — Bring one end of the magnet near a 
few tacks scattered on a piece of paper. Observe carefully 
what happens. Repeat two or three times until you are 
sure that you have noticed all that occurs. Repeat with an 
ordinary piece of steel. Compare results. Try other 
bodies in place of the iron. Do you get the same result ? 

Definitions. — If whenever a body is brought near a piece 
of iron or steel we obtain the results observed above, that 
body is called a magnet. This name is given it not because 
it is made of any particular substance or made in any par- 
ticular shape, but only because when placed under certain 
conditions, for instance those in Experiment 1, certain 



2 MAGNETISM. 

tilings happen that do not happen when other substances are 
placed under the same conditions. Anything that happens 
among physical things (things that have weight or take up 
room) is called a physical phenomenon ; for example, the 
behavior of the tack when the magnet was brought near it 
would be a phenomenon. Placing a body under certain 
conditions and observing the resultant phenomena is called 
an experiment. A magnet in the form of a straight bar is 
usually called a bar magnet. 

EXPERIMENT 2. 

Object. — To see (a) if contact is necessary to get the 
results of Experiment 1, and (b) the effect of interposing 
various bodies between the magnet and the iron. 

Manipulation. — Stand a tack on its head and bring the 
magnet slowly up to it. Note particularly whether or not 
the tack moves before the magnet touches it. Repeat the 
experiment, holding successively a piece of paper, a piece 
of glass, and a thin piece of wood between the end of the 
magnet and the tack. 

EXPERIMENT 3. 

Object. — To see if the magnetism is of the same strength 
all along the bar; and if not, how it varies at different points. 

Manipulation. — Lay the magnet on a sheet of paper 
and dust iron-filings over it all along the bar. Now raise 
the bar. By the number of filings that adhere to the 
various parts of the magnet you can form some idea of the 
distribution of the magnetism. 

EXPERIMENT 4. 

Object. — To see if the distance between the magnet 
and the iron produces any effects. 

Manipulation. — Stand a large tack on its head, slowly 
bring one end of the magnet up to it, and observe the 



GENERAL STUDY OF A MAGNET. 3 

distance between the end of the tack and the end of the 
magnet when the tack begins to move. Repeat with a 
small tack. 

EXPERIMENT 5. 

Object. — To see what happens when iron is brought be- 
tween the magnet and another piece of iron. 

Manipulation. — Lay the magnet so that one end pro- 
jects over the edge of the table. Attach a tack to it and 
then bring a second tack up to the first. Try other sub- 
stances in place of the second tack. 

EXPERIMENT 6. 

Object. — To measure the magnetic pulls at different 
points of the bar. 

Manipulation. — Rest the centre of the magnet on top 
of a bottle or block of 
wood, as in Fig. 1, and 
suspend a tack from one 
end, then carefully at- 
tach a second tack to 
the first, and so proceed 
until you have as long a 
chain of tacks as the 
magnet will hold. Count and record the number of tacks. 
Remove the chain and repeat from a point about one-half 
inch nearer the centre of the magnet. Continue these 
measurements at points about one-half inch apart through 
the length of the magnet. Make a table of your results as 
follows : 




Distance from right-hand end of magnet. 


Number of tacks. 







Holding the magnet vertically, measure in the same 
way its power at the ends. 



4 MAGNETISM. 

Definitions. — The points in the magnet where the mag- 
netism is the strongest are called the Poles. 

When one body moves towards another, as the tack 
moved towards the magnet in Exercise 1, it is said to be 
attracted; thus, instead of saying that the tack moved 
towards the magnet, we would say that the tack was " at- 
tracted " by the magnet. Under the same circumstances, 
if the body moved away, it would be said that it was 



A qualitative experiment is one in which whatever hap- 
pens is simply observed; a quantitative experiment is one in 
which measurements are made. For example, Experiment 
6 in Exercise 1 was quantitative, while all the other experi- 
ments were qualitative. 

"When a body acts as if it were pushed or pulled, as for 
example the tack in Experiment 1, it is said to be acted 
on by & force. 



EXERCISE 2. 

THE ACTION OF THE ATTRACTED BODY ON THE MAGNET. 

Preliminary. — How the iron behaves toward a magnet 
was shown in Exercise 1; now it is desired to find out 
whether the magnet is also affected. When the magnet 
was brought up to the tack, the tack moved; but the 
magnet, if it tended to move, could not do so because it 
was held firmly. In studying the action of the attracted 
body on the magnet, the conditions of Ex. 1 would natu- 
rally be reversed. The magnet would be placed on the table 
and the tack held near it. This could be done if the mag- 
net were very small, but the magnets ordinarily used are 
so heavy that, if the experiment were tried in that way, the 
attraction would have to be very strong in order to move 
them. If, however, the magnet be suspended, it will not 



. ACTION OF THE ATTRACTED BODY. 5 

rub against anything if it tends to move, and even a very 
slight pull will cause it to swing; therefore in the follow- 
ing Exercise the magnet is suspended and a body brought 
up to it. 

EXPERIMENT 1. 

Apparatus.— Bar magnet; a new nail or tack; stirrup and thread 
for suspending the magnet.* 

Object. — To see if the attracted body also attracts the 
magnet. 

Manipulation. — Make a small 
stirrup of wire (copper is the 
best), as in Fig. 2, and by means 
of it suspend the magnet so that 
it swings freely and hangs hori- 
zontally. When it has come to 
rest, bring a large nail near one 
end, but not touching it. Ob- 
serve carefully what happens, and 
record. 

Now repeat with the other end of the magnet. Notice 
particularly whether the results are the same for both ends. 

EXPERIMENT 2. 

Object. — To see what happens when a magnet is free 
to move in a horizontal plane. 

Manipulation. — Set the suspended magnet to swinging 
gently. Note if it tends to come to rest in any particular 
direction, and if so in what direction. . If there is any 
doubt, after the magnet has come to rest displace it slightly 
and see if it shows any tendency to return to that position. 
Does any particular end of the magnet tend to point in any 
particular direction? 

* If a compass is available, it may be conveniently substituted 
for the suspended magnet. 




6 



MAGNETISM. 



Definitions.— If something happens to one substance 
when another substance is brought near it, the second is 
said to act on the first. If the action is mutual, either 
body may be said to act and the other would then be said 
to react. Does a magnet act on a piece of iron ? Is there 
any reaction ? If so, where ? 

The pole of a magnet that tends to point north is called 
the North-seeking or North pole. In the same way the 
other is called the South pole. 

When new properties are developed in one body by bring- 
ing another body near it, the new properties of the first 
body are said to be induced by the second. 

Any contrivance for getting desired conditions is called 
a piece of apparatus; for instance, a compass is a contrivance 
or piece of apparatus for arranging a magnet so that it can 
swing freely. 

When the same experiment has been tried a great many 
times, with the same results wherever or whenever it was 
tried, such results are said to be a law. For example, 
whenever a magnet has been brought near a piece of iron 
that could move, the iron has moved towards the magnet; 
and whenever the magnet has been placed under such con- 
tions that it could move, it has moved toward the iron. 
Whenever this has not happened, it has always been found 
that some other conditions had been introduced into the 
experiment, and when these were removed the usual 
results have taken place; hence it is said to be a law that a 
magnet attracts a piece of iron and the piece of iron at- 
tracts the magnet. 

EXERCISE 3. 

MUTUAL ACTION OF TWO MAGNETS. 

Preliminary.— So far, magnets have been studied; but 
m the following Exercise the subjects are not magnets, but 
magnetic poles, and it is desired to study the action of one 



MUTUAL ACTION OF TWO MAGNETS. 7 

magnetic pole on another. In order to do this, one pole 
must be free to move and. the other must be brought near 
it. As there are two kinds of poles, both like and unlike 
poles must be tried. It is impossible to get the poles alone, 
so whole magnets must be used; and in order to have the 
poles free to move, one magnet must be suspended. The 
same device could be used, as in Exercise 2, but a more 
convenient apparatus is a compass, which consists of a 
magnet supported on a sharp point and contained in a 
circular box, usually provided with a glass cover. 

EXPERIMENT 1. 

Apparatus.— Bar magnet; compass; wood; glass; paper; etc. (as 
in Ex. 1). 

Object. — To study what takes place when two magnetic 
poles are brought near each other, one pole being free to 
move. 

Manipulation. — Take a compass and find the north 
pole (Ex. 2, Exp. 2). Lay the bar magnet on the table 
and bring the north pole of the compass-needle up to the 
north pole of the magnet. In the same way try bringing 
the north pole of the compass-needle up to the south pole 
of the magnet. Try also the south pole of the compass and 
the south pole of the magnet, and the south pole of the 
compass and the north pole of the magnet. Tabulate your 
results as follows : 



Pole of Compass. 


Pole of Magnet. 


Results. 









From the study of the table, write in your note-book the 
" law " of the action of magnetic poles. 

EXPERIMENT 2. 

Object. — To see if the results of Experiment 1 still hold 
when various bodies are placed between the poles. 



8 



MAGNETISM. 



Manipulation. — Repeat Experiment 1 with pieces of 
wood, glass, paper, etc., held between the poles. Tabulate 
results as follows : 



1st Pole. 


2d Pole. 


Body Used. 


Results. 











EXERCISE 4. 

INDUCED MAGNETISM. BREAKING MAGNETS. 
EXPERIMENT 1. 

Apparatus.— Bar magnet; compass; large darning- or knitting- 
needle of quite hard steel; piece of iron wire; copper wire (say No. 
16); large horse-shoe nail; iron-filings; piece of paper on which to 
put the filings; pieces of wood, and glass rod or tubing. 

Object. — To observe the effect of bringing a piece of 

steel in contact with a magnet. 

Manipulation. — Take a large darning-needle and stroke 

one end, always in the same direction, several times on one 
pole of a bar magnet, as shown 
in Fig. 3. Note the nature of the 
pole used. Bring the end of the 
needle that you stroked on the mag- 
net up to a compass-needle. Note 
what change has been produced in 
the darning-needle. Test the 

other end in the same way 

EXPERIMENT 2. 

Object.— To find out how the nature of the inducing 
pole affects the nature of the induced pole. 

Manipulation. — Compare the nature of the pole in- 
duced in the end of the needle that was rubbed on the 
magnet with the nature of the pole on which it was rubbed. 
Test the nature of the poles by the knowledge gained in 
Ex. 3. Test also the other end of the needle. State in 
your note-book the law for the induction of magnetic poles. 



Fig. 3. 



INDUCED MAGNETISM. BREAKING MAGNETS. 9 
EXPERIMENT 3. 

Object. — To see if all substances can be magnetized. 

Manipulation. — Repeat Exp. 2 with the following: 
Soft iron wire which you are sure is not magnetized, wood, 
glass, and copper. Tabulate your results. 

EXPERIMENT 4. 

Object. — To observe the results of breaking a magnet. 

Manipulation. — Break your magnetized needle in the 
centre and, with the compass, examine both ends of each 
part. Record results, and draw figures illustrating them. 

EXPERIMENT 5. 

Object. — To find what happens when the broken parts 
of the magnetare put together again. 

Manipulation. — Bring the broken parts of Exp. 4 
together, opposite poles in contact, and with the compass 
examine it all along its length for magnetism. From these 
results suggest, if you can, why the centre of a magnet shows 
no magnetism. Break one half of your needle and test each 
half as before. As the magnet is broken into smaller and 
smaller pieces, what will apparently be true of each part ? 

EXPERIMENT 6. 

Object. — To see if a change is produced in a piece of 
iron when brought near a magnet. (Compare this with 
Exercises 1 and 2.) 

Manipulation. — Take a wrought-iron horseshoe-nail, 
test it to make sure that it is 
free from magnetism, and then 
hold it vertically with the lower 
end in some iron-fillings; bring 
the magnet over the upper end 
of the nail, but not in contact 
with it. (See Fig. 4.) Lift the 
magnet and nail together, still W 

holding them a little distance FlG * ' 

apart. Observe results. Take away the magnet and again 



10 MAGNETISM. 

observe results. Repeat the experiment with the other 
pole of the magnet. Try putting a piece of paper between 
the magnet and the nail. Put the bar magnet entirely out 
of the way and test the nail for magnetism by means of the 
compass. After a lapse of five or ten minutes test the nail 
again. 

State in your notes anything that you have observed 
regarding the different behavior of iron and steel when 
brought near or in contact with a magnet. If needed, 
Exp. 6 may be repeated roughly, with the nail and the 
magnet in contact. 

Questions. — What tests could you apply to distinguish 
a magnet from a piece of steel ? Why are magnets made 
of steel instead of iron ? 

EXERCISE 5. 

LAW OF INDUCED MAGNETS. 

Preliminary. — When a piece of iron or steel is mag- 
netized by being brought near or in contact with a magnet, 
it is said to be an induced magnet, and the original magnet 
is said to be an inducing magnet. 

The different behavior of iron and steel is expressed by 
saying that the steel has a greater rctentivity than iron. 

The magnetism remaining in a piece of soft iron after 
the inducing magnet has been removed is called residual 
magnetism. 

In the following exercise, we wish to find out how the 
poles of the inducing magnet affect the poles of the in- 
duced magnet. 

EXPERIMENT 1 . 

Apparat as.— Bar magnet; compass; 2 horseshoe-nails, or 2 pieces 
of soft iron wire, 3 or 4 inches long. If nails are used, they will prob- 
ably have to be new ones, as the nail used in Exercise 4 will probably 
retain some magnetism. 

Object. — To study the nature of the poles of the induced 



LAW OF INDUCED MAGNETS. 



11 



magnet, and discover how they are related to the poles of 
the inducing magnet. 

Manipulation. — Arrange apparatus as in Fig. 5, where 
AB represents the bar magnet, CD represents a soft iron 



]F 




nail (free from all magnetism), and NS represents the 
compass. Be sure that the direction in which the nail and 
magnet lie is an east and west one, i.e., at right angles to 
the normal position of the compass-needle. Starting with 
the magnet three or four inches from the end of the nail, 
slowly bring it up to the end G. Note how the end D 
affects the north pole of the compass-needle. Eepeat, 
using the south pole of the magnet. State in your notes 
how you find the pole of the induced magnet at the end 
furthest from the pole of the inducing magnet to compare 
with the inducing pole of the inducing magnet. Illustrate 
by a diagram. 

EXPERIMENT 2. 

Object. — To discover the nature of the induced pole 
nearest to the inducing pole. 




Fig. 6. 

Manipulation. — Arrange apparatus as in Fig. 6. 

The distance from the pole of the magnet to the pole of 



12 MAGNETISM. 

the compass-needle should be about an inch. When the 
nail is brought close to the pole, it becomes an induced 
magnet and, if suddenly removed from the pole, retains its 
magnetism for an instant. (See Ex. 4, Exp. 6.) When the 
compass-needle is at rest, suddenly move the end of the nail 
which is in front of the magnetic pole up to the compass. 
The induced pole in the nail, remaining for an instant, is 
brought so much nearer to the pole of the compass that 
its action is noticeable, in spite of the greater action of the 
pole of the bar magnet.* 

EXERCISE 6. 

LINES OF MAGNETIC FORCE. 

Preliminary. — We know from previous experiments that 
I the space around the poles of a magnet is in 
such a condition that a body which can be 
magnetized is acted upon when brought into 
that space. This space is called the field of a 
magnet. If the body moves towards the magnet, 
it moves in the direction of the force, that is, in 
the direction in which the magnetic push or 
pull is exerted. Suppose a small piece of iron 
placed near a magnetic pole, as in Fig. 7. It is 
magnetized by induction and becomes a magnet. 
The end nearest the inducing magnet will be, 
as shown in the figure, a pole opposite to the 
nearest pole of the inducing magnet. The pole 
farthest from the inducing pole will be like it. The bit 
of iron will be attracted at one end and repelled at the 
other end with practically equal force, hence it will not 
tend to move toward the magnet, but will swing around 
until its length lies in the line of the push and pull. 

To illustrate this, imagine a stick lying on the floor, 

* Suggestion. — Prepare an essay on Induced Magnetism. 



LINES OF MAGNETIC FORGE. 



13 



with a string attached to each end, as in Fig. 8. On 
pulling both strings the stick will not move in either 



direction, but will twist around on its centre until it lies 
in the line in which the strings were pulled, as in the 
second diagram. 

The lines marking the direction of the magnetic push 
or pull are called lines of magnetic force. In the follow- 
ing exercise we wish to observe these lines for various cases. 

EXPERIMENT. 

Apparatus— A. piece of sized writing-paper; fine iron-filings; 
two bar magnets; shellac; glass tube; blocks of wood. 

Object. — To study the lines of magnetic force. 

Manipulation. — Take a piece of glazed paper, and 
pour fine iron-filings on it. Pour off the iron-filings and 
you will find that a layer of iron-dust remains on the paper. 
Lay a bar magnet on the table, hold the paper horizontally 
over it and then bring it straight down until it rests upon 
the magnet. If the magnet can be placed between two 
blocks of wood whose thickness is the same as the depth 
of the bar, so that the paper lies on a level surface, better 
results can be obtained. Tap the paper very gently with 
a lead-pencil and the little particles of iron will swing 
around on their centres until they everywhere lie in the 
line of the magnetic force. There will also be a number of 



14 MAGNETISM. 

lines on the paper which surround the outline of the mag- 
net. These lines are called lines of force, and each line 
represents the line of the magnetic force in its part of the 
field. If a good set of lines is not obtained with one or two 
gentle taps, remove the paper and try again, as continual 
tapping will only cause the iron particles to bunch. 

The positions taken by the iron-filings now give the 
diagram of the lines of force, and in order to study them 
they must be preserved in some way. 

Method 1. Lift the paper vertically off the magnet to a 
height of about 6 inches, then gently place it on the table 
and carefully copy on another piece of paper the diagram 
obtained. 

Method 2. With a lead-pencil trace out the different lines 
one after another on the paper itself. On wiping off the iron- 
dust you will have a fairly good reproduction of the lines. 

Method 3. If it is desired to preserve in place the parti- 
cles of iron themselves, there will be needed, in addition 
to the other apparatus, some thin shellac and a glass tube, 
open at both ends, about £ in. internal diameter and 3 in. 
long. Holding this tube as in Fig. 9, insert one end into 
the shellac and remove the finger from the top for an 
instant. Replace the finger and lift the tube from the 
liquid. So long as the finger is pressed on the top of the 
tube some shellac will remain inside and may be allowed 
to run out by raising the finger. With the paper lying 
upon the magnet, rest the tube very gently on the paper 
cv just inside the outline of the 

I i^Y\ 7 magnet (at the point marked 

/ /''J^Y ) I x in Fig. 9), inclining it 

i I — i'~'m&-i\*\ I a ^ an an gl e °f about 45°. 

/ "\"\'\ \ » / After it is on the paper, 

/ x ^ v " / but not before, remove the 

FlG - 9 - finger, thus allowing the 

shellac to run out. The rate at which the shellac flows 



LINES OF MAGNETIC FORCE. 15 

may be regulated by the degree to which the finger is 
removed. Care must be used to prevent the shellac from 
running out with sufficient force to move the iron parti- 
cles. If the operation is properly conducted, the particles 
will not be disturbed and the shellac will soak in among 
them. If the first application of shellac does not en- 
tirely cover the figure, more may be added, with the same 
precaution, at other parts of the paper. The greatest 
care must be used not to allow any of the liquid to drop on 
the paper, as it will displace the iron-dust where it strikes. 
When the operation is completed, it is best to leave the 
paper until the alcohol has evaporated, which may be in 
five or ten minutes. During this time be careful that the 
paper is not disturbed. If in a hurry, the paper may be 
lifted vertically from the magnet and placed upon a hori- 
zontal surface until dry. When the shellac has become 
hard the iron is permanently fixed and the figure may be 
pasted in the note-book. 

Method 4. For this the shellac should be somewhat 
thicker than in the preceding method. Place the paper 
over the magnet and pour the shellac on the paper, allow- 
ing it to spread out in a thin layer. Then carefully scatter 
the iron-dust over it and the iron particles will spread 
in the shellac, on which they will float. Tap gently until 
the lines appear, and allow the paper to remain undisturbed 
until dry. 

By one of these methods obtain the lines of force in the 
following cases: 1. A north pole. 2. A south pole. 
3. Two like poles. (Use two bar magnets end to end, the 
ends being about half an inch apart.) 4. Two unlike 
poles, arranged in the same way as in 3. 

Questions. — 1. What is the form of the lines of force 
around a single magnetic pole ? 2. What is the shape 
of the lines of force around two like poles situated near 
each other? 3. What is the shape of the lines of force 



16 MAGNETISM. 

around two unlike poles situated near each other ? 4. 
How does the form of the lines of force around two like 
poles compare with the form of the lines of force around 
two unlike poles ? 5. In what case are the lines continu- 
ous from pole to pole, and in what case are they not ? 
6. How do the lines of force compare around a north or 
south pole when no other poles are near ? 



CUEEENT ELECTRICITY. 
EXERCISE 1. 

VOLTAIC ELECTRICITY. 

Introductory. — The word Electricity is the name given 
to the cause of certain phenomena, just as Magnetism is 
the name given to the cause of certain other phenomena, 
such as the attraction of iron and steel by a magnet or the 
attraction and repulsion of magnetic poles. 

When chemical, as well as some other changes are pro- 
duced under certain conditions, the resulting phenomena 
are said to be caused by electricity. When these phenom- 
ena are produced by chemical change, they are said to be 
due to current or voltaic electricity. In the following 
exercises some of these phenomena are observed, the con- 
ditions under which they can be brought about in- 
vestigated, and some points connected with the useful 
applications of electricity examined. 

EXPERIMENT 1. 

Apparatus.— 5 test-tubes ; a bit of zinc ; a copper tack ; an iron 
nail ; a piece of carbon (electric-light carbon or piece of old battery 
carbon); a piece of amalgamated sheet zinc; copper and zinc strips; 
diluted sulphuric acid ; compass ; tumbler ; some means of sup- 
porting the tubes in an upright position; bar magnet. 

Object. — To observe the action of dilute sulphuric acid 
on a number of substances.* 

Manipulation". — Take 5 test-tubes and in each place 
5 cc. 10$ t sulphuric acid. Place in each tube one of 

* Much time can be saved by working this experiment simul- 
taneously with Experiment 2. 

f One part of strong acid to nine parts of water. 

17 



18 CVRRENT ELECTRICITY. 

the following substances: zinc, copper, iron, carbon, and 
a bit of zinc which has first been wet with acid and then 
rubbed with mercury.* From time to time during 15 or 
20 minutes, watch carefully what goes on and record your 
observations. Watch particularly for answers to the fol- 
lowing questions, but make in addition a complete record 
of all that takes place. 

Questions. — 1. Does any change go on ? 2. If so, is it 
the same in all the tubes ? 3. Has there been any change 
in the size of the bodies ? 4. Arrange the names of the 
bodies in the order of the energy of the action, beginning 
with the body acted on the least and ending with that 
acted on the most.f 5. In any of the tubes is there any 
change in the nature of the action after it has gone on for 
a while ? If such a case is noted, make a careful record of 
all that is observed in connection with it. 6. Summarize 
what has been learned regarding the action of cold dilute 
sulphuric acid on various substances. 

EXPERIMENT 2. 

Apparatus.— Strip of copper, strip of zinc (unamalgamated), with 
wires; a tumbler ; dilute sulphuric acid ; compass. 

Object. — To observe how electricity is produced from 
chemical action. 

Manipulation. — You are provided with two strips, one 
of copper and one of zinc, a copper wire being attached to 
each. Place these strips in the tumbler and pour in 10$ 
sulphuric acid until the plates are covered to a depth of 
about two inches. The acid must not be deep enough to 
cover the points where the wires are attached to the plates. 

* Zinc so treated is said to be amalgamated. 

f The bubbles of air which may slowly come out of some of the 
bodies, particularly the carbon, are not to be confounded with the 
bubbles of hydrogen gas given by the chemical action. The air has 
no smell, the hydrogen has. On thrusting a lighted match into 
hydrogen the gas will usually burn. 



VOLTAIC ELECTRICITY. 



19 




Fig. 10. 



During this operation, do not allow the strips to come in 
contact. To prevent this, before pouring in the acid 
arrange as in Fig. 10, bending the wires back so as to 
spring against the sides, 
thus holding the two plates 
on opposite sides of the 
tumbler. Note carefully 
what happens on each 
plate, then bring the wires 
in contact, watching each 
plate carefully while you 
do so. Lay the compass on 
the table and arrange ap- 
paratus as in Fig. 11, so that when the compass-needle is 
at rest, one of the wires lies directly beneath and parallel to 

it. While arranging this, 
the wires must not be in 
contact. Now connect the 
ends of the wires.* What 
goes on in the tumbler ? 
What goes on in the com- 
pass ? Disconnect the 
wires and, when the compass-needle has come to rest, hold 
a bar magnet about six inches above it. Bring the magnet 
slowly down to the compass, watching the needle as you do 
so. Find in what direction the 
magnet must be held, and how 
it must be moved to produce the 
same effect on the compass- 
needle that was produced by (1) 
connecting the wires, (2) discon- 
necting them. How could a 
number of magnets be arranged so as to produce the same 

* Should any marked phenomena fail to appear on bringing the 
wires in contact, remove plates, clean carefully, and repeat. 





20 CURRENT ELECTRICITY. 

effect on the compass as was produced by the wires ? 
lustrate by a sketch in your note-book. 



EXERCISE 2. 

CONDITIONS FOR PRODUCING CURRENT. 

Preliminary. — When, on bringing a wire near a compass- 
needle, or any magnet free to deflect, a phenomenon like 
that in the preceding exercise is observed, the wire is said 
to have a current of electricity flowing through it. We 
do not know exactly what goes on in the wire, or why 
the needle acts as it does; and when we say that a wire 
is carrying a "current" we only mean that, if the wire 
were brought near a compass-needle, the needle would be 
affected as we have observed in the preceding exercise. 
The wire is the same wire whether it "carries a current" 
or not. When, for example, one plate is lifted from the 
liquid, the power of the wire to twist the needle dis- 
appears. This also happens if the wire is not complete 
from one plate to another. But while we do not change 
the wire, we do change the conditions under which the 
wire is placed. Hence when we speak of a wire carrying a 
current we imply a special condition of the wire. The steps 
necessary to develop in a wire the power indicated by the 
compass-needle are called the conditions needed for the pro- 
duction of an electric current. As will be seen later, there 
are other ways in which this condition of the wire may be 
brought about besides that of the galvanic cell ; but no 
matter what has been done to a wire, if it can do what the 
wire in the preceding exercise could do, it is said to carry a 
current while in that condition, and at no other time. 

Question's. — Define electricity; an electric current. How 
could you determine whether a telegraph-wire was carrying 
a current or not ? Name any method for generating elec- 



CONDITIONS FOR PRODUCING CURRENT. 21 

tricity besides the chemical one. Must anything be de- 
stroyed in order that the current may be generated ? 

Diagrams. — Figs. 11 and 12 both represent the set of 
apparatus used in this exercise. On examining them, 
however, you will see that Fig. 11 is a picture of the ap- 
paratus, showing it as it actually looks, while Fig. 12 bears 
no resemblance to it at all. In Fig. 12 the tumbler and 
plates are represented by a circle with two lines inside, the 
compass by a circle with a long diamond inside, and the 
wires by lines. It is not necessary to show what the 
tumbler looks like, or what the compass looks like, or what 
sort of wires are used; the essential thing is to make clear 
that the wire connecting the plates is carried under the 
compass in a north and south line, and this is done just 
as well in Fig. 12 as in Fig. 11. Such a figure as Fig. 12, 
which only shows the way in which the parts of the appa- 
ratus are arranged to bring about the conditions under 
which the experiment is worked, is called a diagram; and as 
diagrams are much easier to draw, in scientific work they 
are often used in place of pictures. 

In making diagrams, each instrument has its own sign. 
Where a picture of an instrument is given in this book, 
the sign by which it is to be represented in diagrams is 
also given (for example, see Figs. 13 and 14). Unless 
otherwise instructed, always represent apparatus by dia- 
grams in your note-book, and the instruments by the 
regular signs. Use a ruler whenever you can, and be care- 
ful to make the diagram large enough. A space at least 
3x3 inches, and often even half a page or a whole page of 
your note-book should be used. A space reserved for a 
diagram should never have notes written in it. In a dia- 
gram the different parts are usually indicated by letters, 
generally the initials of the names of those parts ; thus a 
compass is marked C, a wire W, etc. Where the same 
letters have to be used more than once, one or more accents 



22 CURRENT ELECTRICITY. 

are added. For example, if two wires were to be marked, 
they would be lettered W and W (W prime), respectively, 
and a third wire would be marked W" (W second). Or 
capitals and small letters might be used. 

EXPERIMENT 1. 

Apparatus.— Copper strip ; zinc of "tumbler cell" (amalga- 
mated) ; tumbler ; compass ; dilute acid ; iron plate ; carbon plate 
of cell ; water; nail; wood; glass; etc. 

Object. — (a) To observe the effects, in the tumbler and 
on the compass-needle, of amalgamating the zinc, (b) To 
study the conditions under which this effect on the com- 
pass-needle can be produced. 

Manipulation. — Part I. Proceed as in the preceding 
exercise, noting carefully what goes on in the tumbler with 
amalgamated zinc, the wires first in contact, then not in 
contact. Repeat the test with the wire and compass. 

Questions. — What effect has the amalgamation of the 
zinc on (1) the action in the tumbler when the wires are 
not in contact ? (2) the action in the tumbler when the 
wires are in contact? (3) the action of the wire on the 
compass-needle ? 

Part II. (a) Bring the wires in contact and, holding 
one wire over the compass, cause the needle to deflect. 
Still holding the wire over the compass, separate the ends 
(it is well to tap the compass gently, as the needle is 
liable to stick). Having again caused the needle to deflect, 
raise one plate from the liquid. Note what happens in 
the compass and in the tumbler. Replace the plate, watch- 
ing carefully for any changes. Try the other plate, (b) 
As regards the nature of the liquid: replace the acid in 
the tumbler by water, trying the compass test and watch- 
ing the tumbler carefully, (c) As regards the relation of 
the plates to the liquid : place in the acid two strips of 



CONDITIONS FOR PRODUCING CURRENT. 



23 



zinc, also try two strips of copper.* Repeat the compass- 
test. Try other metals — zinc and iron, zinc and carbon, 
iron and carbon. In each case try the compass-test and 
watch carefully what goes on in the tumbler. 

Questions. — 1. Can the compass-needle effect be pro- 
duced with any two plates ? 2. Do the plates all produce 
the same effect? If not, name them in the order of the 
amount of deflection they produce. 3. Is any change notice- 
able in the plates as the action goes on ? If so, where ? 
4. Can the plates be connected by any substance ? Lay a 
nail over the compass and touch the ends of the wires one 
to each end. Try in the same way wood, glass, wire, etc. 
Note the behavior of the compass in each case. (5) What 
conditions, then, must be fulfilled in order that the mag- 
netic needle shall be deflected by the wire as regards (a) 
the wire, (b) the plates, (c) the liquid, (d) the magnetic 
needle ? 

Supplementary. — An arrangement of plates, liquid, etc., 
fulfilling the conditions found in the this exercise, is called 




a galvanic cell. The plates are called the elements or 
plates. The fluid is called the exciting fluid. The 

* Exchange strips with your neighbor. 



24 



CURRENT ELECTRICITY. 



wires leading from the plates are called the conductors, or 
the leadiug wires. One form of cell is shown in Fig. 13. 
The plates of carbon (C) and zinc (Z) are separated by 
pieces of wood (WW) and held in place by a rubber band 
(RR). The plates are set in a glass vessel to contain the 
exciting liquid, and to each plate is attached a wire, as 
shown in the figure. In diagrams a cell is usually indi- 
cated by two parallel lines of unequal length, as B in Fig. 
14, which would represent 
one cell. The connecting 
wires are indicated by straight 
lines, as shown, while arrows 
near the lines indicate the 
direction of the current. 
When the cell is so arranged 
that the current is passing 
through the conductors, as in 
Fig. 14, the cell is sometimes 
said to be running. Although 
FlG - 14 - we only know that the wires 

possess certain properties when the cell is running that 
they do not possess when the cell is not running, it has 
been customary to imagine that electricity flows through 
the wire, and to speak of a current of electricity We have 
no means of finding out which way this current flows, 
but it is generally considered as flowing in the wire con- 
necting the plates from the metal least acted upon to that 
most acted upon, and through the liquid in the cell in the 
reverse direction. The plate from which the current is sup- 
posed to flow in the wires is called the positive plate, and is 
indicated by the + sign. The plate to which the current 
flows is called the negative or minus plate, and is indicated 
by the — sign. The whole path of the current, plates, 
liquid, and conductors is called the circuit. 







> 1 r 




\ B 





ACTION OF CURRENTS ON MAGNETS. 



25 



EXERCISE 3. 

ACTION OF CURRENTS ON MAGNETS. 

EXPERIMENT 1. 

Apparatus.— About 100 cm. of No. 18 insulated copper wire ; com- 
pass ; electric current. Tumbler-cell. Supports for compass. 

Object. — To study the conditions affecting the behavior 
of a magnetic needle free to move, when near an electric 
current. 

Manipulation". — 1. Place the wire over the needle in a 
north and south line, arranging the wire so that the cur- 




rent flows from north to south. Complete the circuit and 
note the direction of the swing of the needle. 2. Eepeat 
with the wire directly under the needle. 3. Repeat 1 with 
the current reversed, that is, flowing from south to north 
over the needle. 4. Eepeat 2 with the current flowing 
from south to north. 5. Place the compass on a tumbler 



26 CURRENT ELECTRICITY. 

or block of wood as shown in Fig. 15. Hold the wire 
vertically, due north from the compass, with the current 
flowing down, and bring it slowly up to the north pole. 
6. Repeat 5, holding the wire due south of the compass and 
bring it up to the south pole. 7. Invert the wire so that 
the current flows up, and repeat 5. 8. Repeat 6, the 
current flowing up. 9. Wind the wire tightly around the 
compass so as to form a rectangle. Hold this rectangle 
vertically in a north and south line ; place the compass in 
the centre of the rectangle. 10. Eepeat 9 with a loop 
instead of a rectangle. 11. Observe the effect of using 
more than one loop, by winding the wire around the com- 
pass once, then 5 or 6 times. 12. Observe the effect of the 
size of the loops. Try a large loop and a small one, keep- 
ing the compass in the centre of each. 13. Observe the 
effect of the distance of the wire from the needle. 

Questions. — 1. Illustrate each case by means of a dia- 
gram. 2. What conditions affect the direction of the 
swing of the needle ? 3. If a man were swimming in the 
current so that it enters his feet and leaves his head, he 
always facing the needle, to which hand, right or left, 
would a north-seeking pole be urged ? * A south-seeking 
pole ? If you cannot tell, put yourself in the place of the 
imaginary man by holding the wire in front of you, or 
make a little paper man, marking the right and left hands, 
and, holding it in the position described, move it around 
the loop, observing towards which of his hands the north 
pole of the needle is deflected. In marking the hands of 
the paper man, do not forget that if he faces you his 
hands would be the opposite of yours, that is, his left 
hand would be opposite your right. 4. What conditions 
affect the amount of the swing? 5. Remembering that 

* Notice that we are dealiug here with poles, not with entire 
magnets. 



ACTION OF CUtiKENTS ON MAGNETS. 27 

the needle always tends to place itself in the line of mag- 
netic force, from a study of the diagrams make a diagram 
of the field of force around a wire carrying a current. 

The Galvanometer. — The law connecting the direction 
of the swing of the needle with the direction of the cur- 
rent is called Ampere's law. Advantage of this law is 
taken in constructing an instrument for observing the 
direction and strengths of electric currents. The in- 
strument is called a galvanometer, and consists of a 
magnetic needle placed in the centre of a coil of wire and 
arranged so as to move freely. When this coil is placed in 
a north and south line and a current is passed through it, 
the needle is deflected. The direction of the deflection 
indicates the direction of the current, while the degree of 
the deflection indicates the relative strength of the cur- 
rent. In a general way, the stronger the current, the 
greater the deflection. 

We found that with a given current the amount of deflec- 
tion could be changed by varying the number of turns of 
wire. In most galvanometers this is done by changing 
the connections. With a very heavy current, but few 
turns would be needed ; with a weak current, more turns 
would be required to give readable changes in the position 
of the needle for small differences in current. Of course, 
in comparing various currents, the same number of turns 
must be used. 

Fig. 16 is a representation of a galvanometer. The coil 
of wire IF is wound upon a wooden hoop, H, which, is sup- 
ported in an upright position by the base-boards E and D. 
This coil is connected with the three binding-posts B, B' , 
B" . Starting from B, the wire passes once around the 
hoop and is led out to B' . It then is wound around the 
hoop nine times more, so that if B and B' be connected, 
the current passes around the hoop once ; if B' and B", 
the current passes through nine turns; while if B and B" 



28 



CURRENT ELECTRICITY. 



be connected, ten turns are in circuit. A compass 
placed in the centre of the hoop furnishes the magnetic 
needle whose indications are observed, the scale on the 
compass providing a means of measuring the amount of the 




swing. A galvanometer is represented in diagram by the 
small figure on the left. This sign does not represent 
simply this form of galvanometer, but any form. 

Precautions. — 1. The compass must be in the centre 
of the hoop. 2. The coil must be in a north and south 
line. 3. There must be no iron or magnets near. 4. All 
contacts must be good. 5. Before reading tap the hoop 
gently, as the needle may stick. 6. In reading hold the 
eye as nearly as possible vertically over the needle. 7. The 
end of the needle when at rest should be directly over the 
zero of the scale. 8. When using the galvanometer con- 
nect it for ten turns, unless the instructions state other- 



ELECTRICAL RESISTANCE. 29 

To eead by "Revebsal." — As getting the zero of the 
scale just under the end of the needle requires quite nice 
adjustment and takes time, it is better to read the instru- 
ment by what is known as the "reversal method." Adjust 
the instrument, having the coil nearly north and south and 
the zero of the scale within five degrees or so of the posi- 
tion taken by the end of the needle when at rest. Close 
the circuit, read; reverse, and read again.* The average 
of the two readings will be the true deflection. This 
method saves time and is more accurate. It should be 
used whenever current strengths are to be compared. 

EXERCISE 4. 

CONDITIONS AFFECTING ELECTRICAL RESISTANCE. 

Preliminary. — When a circuit is so arranged that the 
current can pass entirely through it, it is said to be 
" closed," and a circuit so arranged is called a closed cir- 
cuit. When the current cannot pass at any point, the cir- 
cuit is said to be " open," or "broken," and such a 
circuit is called a broken or open circuit. Connecting 
two points on a circuit so as to close it {e.g. bringing 
the ends of the wires together) is called closing the 
circuit or making the circuit; separating two parts of 
a closed circuit, so as to open it (separating the ends of 
the wires, lifting one plate from the liquid, etc.), is 
called breaking the circuit or breaking contact. Sep- 
arating two parts of a circuit and attaching the ends to 
a conductor (as a wire or a piece of apparatus), so as to 
include it in the circuit, is called introducing that body 
into the circuit. 

When several cells are arranged so as to give a current 

* If no reverser is used, this may be done by changing the con- 
nections at the binding-posts. 



30 CURRENT ELECTRICITY. 

they are called a galvanic battery, or simply a battery. 
That part of the circuit which connects the plates out- 
side of the vessel is called the external circuit, and the 
part inside of the vessel is called the internal circuit. 

We have already observed that when various bodies 
were inserted in the external circuit of the same cell, and 
the wires were laid over the compass at the same dis- 
tance from the needle, the deflections of the needle were 
not the same. We have also learned that the amount of 
this deflection is, under similar conditions, taken as indi- 
cating the strength of the current. We naturally infer that 
all bodies do not possess to the same degree the property of 
allowing the current to pass. This idea is expressed by 
saying that the relative conductivity, or, more commonly, 
the resistance, of all bodies is not the same. A body 
that will transmit but little current is said to have a high 
resistance; one that will transmit considerable current is 
said to have a loiv resistance.* Resistance, then, may be 
taken to indicate the degree to which a body possesses 
the property of not transmitting the current. In the fol- 
lowing exercise we wish to find out — 

1. What sort of bodies have high, and what sort low, 
resistance. 

2. What effect length, material, and cross-section have on 
the resistance of bodies. 

EXPERIMENT 1. 

Apparatus.— For Part I : Cell; galvanometer ; connecting wires ; 
coil of copper wire ; iron nail ; pieces of zinc ; carbon ; wood ; 
glass rod ; dilute sulphuric acid and water ; tumbler. For Part II : 
In addition, mercury cups ; reverser ; wire coils. 

Object. — To study (1) the power of various bodies to 
transmit the current, and (2) the conditions effecting this 
power. 

* Of course, uuder the same conditions regarding cell, distance 
of wire from maguetic needle, etc. 



ELECTRICAL RESISTANCE. 



31 




Manipulation. — In Fig. 17, B represents a cell and G a 
galvanometer. One wire from 
the cell connects with the 
binding-post on the galvan- 
ometer. A wire leads from 
the galvanometer connected fig. it. 

so that 10 galvanometer-turns are in circuit. If, now, the 
ends of wires x x' are pressed on any substance, the circuit 
is completed. The ends of the wires should be scraped 
bright and free from insulation, and all contacts made per- 
fect. The screws in the binding-posts should press firmly on 
the wires. These precautions are important. Set up the ap- 
paratus and show it to the instructor before beginning the 
experiment. The galvanometer must be carefully read 
according to the instructions already given. 

Part I. — Tabulate the results of inserting the following 
bodies, in turn, into the circuit : iron, copper, zinc, carbon, 
wood, glass, paper, water,* dilute sulphuric acid, etc., re- 
cording results as follows: 

TABLE I. 



Substance. 


Galvanometer Reading. 


1. 





Part II. — Introduce the mercury-cup, M. 0., into the 
circuit by attaching the ends to the binding-posts, one 
end to one post, as in Fig. 18. To introduce coils of wire 
into the circuit, dip one end well down into the mercury in 
one cup, and the other end into that in the other cup. Lay 
the card on which the coil is mounted flat on the table, 
and bend the ends of the wires so that they will not spring 
out of the mercury while the galvanometer is read. When 

* To test the water, place the naked ends of the wires in a tumbler 
of water. Note and record anything going on in the tumbler, as 
well as the reading of the galvanometer. Then add to the water 10 
or 12 drops of sulphuric acid, and repeat your observations. 



32 



CURRENT ELECTRICITY. 



two single ends, a a, Fig. 19, are placed in the cups, 
there are 10 meters of wire in circuit. When one single 
end, a, and one twisted end, b, are in the cups, there are 
5 meters in the circuit. The coils are labelled, and con- 




M.C. 
Fig. 18. 

sist of, 1, 5 and 10 yards No. 28 copper wire ; 2, 20 yards 
No. 28 copper wire; 3, 5 yards No. 24 (larger cross-section) 
copper wire ; 4, 5 yards German-silver wire, No. 24 or No. 
28, as labelled, same cross-section as one of the coils of 
copper wire of 5-meter length. Insert in turn 5, 10, 20 




Fig. 19. 

yards No. 28 copper wire, 5 yards No. 24 copper wire, 
5 yards German-silver wire. Record results in : 

TABLE II. 



Material. 


Length. 


Cross-section. 
(By number.) 


Galv. Read. 











ELECTRICAL RESISTANCE. 33 

Questions. — Write in your note-books what has been 
learned as regards: 1. The equal resistance of bodies. 
2. The sort of bodies that seem to have the highest resistance, 
and the sort that seem to have the lowest. 3. The resist- 
ance of water and the effect of adding acid. 4. The condi- 
tions affecting the resistance of a body. 5. The reason why 
the wires are of copper. 6. The reason why they are covered 
with cotton, etc. 7. The reason why the covering must be 
removed where connections are made. 8. Give a definition 
of resistance. 9. What part of the circuit has been used 
in this experiment ? 10. Has anything been observed at 
the ends of the wires on making and breaking circuit ? If 
so, what ? 11. What goes on, so far as you have observed, 
when the current is passed through water ? Or through 
water and acid ? 12. Arrange the names of all the bodies 
that you have examined in a list, commencing with those 
of the highest and ending with those of the lowest resist- 
ance. Include air in this list. 

EXERCISE 5. 

ELECTRICAL RESISTANCE. 

Preliminary. — If we wish to insert more than one con- 
ductor into the external circuit, connection can be made in 
two ways; either end to end, or side by side, as in Fig. 20. 

. -»- 

+ T51TU1T 

•4" — Vv>WY 



The first arrangement is called connecting in series, and 
the second connecting in parallel, or in 7nultiple arc. The 



34 



CURRENT ELECTRICITY. 



question is naturally suggested whether, with the same 
bodies, it makes any difference to the total resistance of the 
circuit which method is used. Write out the general 
method * of an experiment to answer this question, outline 
a special method, using the apparatus of the preceding 
exercise, and give the reasons for the use of each part of 
the apparatus. Prepare a diagram showing the relation of 
the parts, connections, etc. 

EXPERIMENT 1. 

Apparatus.— The same as in Ex. 4 (reverser) shown in Fig. 21, the 
mercury-cups being used to insert the various conductors in the cir- 
cuit. 




* The general method is a brief statement of the bodies experi- 
mented upon and of the conditions under which they must be placed 
in order to fulfil the object of the experiment. As different forms 
of the bodies may be used, and as the required conditions may be 
brought about by various means, the special method is a statement 
of just what forms of the bodies are used and just how these forms 
are placed under the conditions required by the experiment. The 
general method might be taken as the plan and the special method 
as the particular way in which the plan is carried out. 



ELECTRICAL RESISTANCE. 



35 



Object. — To see if the manner in which conductors are 
placed in the external circuit affects the resistance of the 
circuit. 

Manipulation.— Part I. Place in the circuit 20 meters 
No. 28 copper wire. Observe the deflection. Remove one 
end, attach to it, by twisting, one end of the 10-meter coil 
of No. 28 copper wire, and place the free end of the IO- 
meter coil in the mercury-cup. There are now in all 30 
meters No. 28 wire in the circuit. Observe the deflection. 
Add to the other two coils the coil of No. 24 copper wire. 
Insert also the coil of German-silver wire. Eecord results 
as follows: 



No. of Trial. 


Lengths and Substances Used. 


Galvanometer Reading. 






Right. 


Left. 


Average. 









Part II. Place the coil of German-silver wire in the 
circuit and read the galvanometer. Without removing 
the first coil, also put in the circuit the 20 meters of 
copper wire. The current can now pass through both 
coils at the same time. Eead the galvanometer. Also 
place in the circuit 5 meters No. 24 copper wire, in addition 
to the others. Eecord the results as above. Great care 
must be used in securing the contacts in the mercury- 
cups, and all precautions should be taken to get as accu- 
rate galvanometer-readings as possible. 

Questions. — 1. What effect is produced on the resist- 
ance of the external circuit by introducing conductors (a) 
in parallel ? (b) In series ? 2. Explain this result from 
the knowledge obtained in the preceding exercise. 3. Can 
the external circuit be composed of more than one sort of 
material ? 



36 



CURRENT ELECTRICITY. 



EXERCISE 6. 

METHODS OF CONNECTING GALVANIC CELLS. 

Preliminary.— When more than one cell is to be used, 
there are two ways of connecting them ; as in Fig. 22, where 

the positive plate of 
one is connected with 
the negative plate of 
the next; or, as in Fig. 
23, where all the posi- 
tives are connected by 
one wire and all the 
negatives by the other. 
The former method 
is called connecting in 
series; the latter, con- 
necting in parallel, or 
multiple. Now, the 
external resistance 
may be either com- 
paratively high or low. 
For instance, the con- 
ductor may be a short, 
thick piece of copper 
wire, or a considerable length of fine German-silver wire. 
Hence it is a matter of some consequence to know which 
method of connection gives the most current, (a) when the 
external resistance is high, and (b) when it is low. 

EXPERIMENT 1. 

Apparatus.— Two cells; galvanometer; reverser; mercury-cups; 
short piece of thick copper wire; connecting wires (connecter, if 
available); wire-coil for high resistance. 

Object.— To determine which method of connecting cells 
gives the most current, (a) when the external resistance is 
high, and (6) when it is low. 




METHODS OF CONNECTING GALVANIC CELLS. 37 

Manipulation. — Insert a galvanometer (one turn) and 
mercury-cups into the circuit of a single cell, as in Fig. 24. 
Connect the two mercury-cups with a short piece of copper 
wire and read the galvanometer. Disconnect the wire 
leading from the cell to the binding-post of the mercury- 
cup (marked a in Fig. 24), and by means of the connecter, 



-I / V- 




B 


Ky 




a 




a * 




OO 





Fig. 24. 



or by twisting the ends of the wires together, connect it with 
the wire leading from the opposite element of the second 
cell. Attach the other wire of the second cell to the empty 
binding-post of the mercury-cup. There are now two cells 
in circuit, the carbon of one connected with the zinc of the 
other — that is, the cells are in "series," as in Fig. 25. 
Connect the mercury-cups with the short piece of wire and 
read the galvanometer. The resistance of the external cir- 
cuit is that of the connecting wires, the galvanometer con- 
nection, the mercury in the mercury-cup, and the short 
piece of wire connecting them ; and as these are all good 
conductors, large and short, the total resistance of the ex- 
ternal circuit is very small. 

Take out the short piece of copper wire connecting 
the mercury-cups, and put in its place a coil of G-er- 



38 



CURRENT ELECTRICITY. 



man-silver wire or 20 meters of No. 28 copper wire. 
This makes the resistance of the external circuit quite 
high. Change the galvanometer connections so as to have 
ten turns, and read the instrument. 'Leaving the coil of 




V^r- 



B 2 



wire in the circuit, disconnect cell No. 2 (B,) and con- 
nect cell No. 1 (B 2 ) alone with the mercury-cups. Read 
the galvanometer. 

Connect the carbon plates of both cells with a wire lead- 
ing to the galvanometer, as in Fig. 26. In the same way 
connect both zinc plates with the same binding-post on the 




mercury-cup. The two cells are now connected in "paral- 
lel." Read the galvanometer. Replace the coil of wire in 
the mercury-cup by the short copper wire. Connect the 
galvanometer for one turn and read it. Arrange results as 
follows : 



METHODS OF CONNECTING GALVANIC CELLS. 39 

TABLE. 



No. of Cells. 


How Connected. 


External Resist. 


Galv-read. 


1 




High 


R. 


L. 


Av. 


2 


Series 


" 








2 


Parallel 


" 








1 




Low 








2 


Series 


" 








2 


Parallel 


" 









The cases in the table are not arranged as they are tried 
in the experiment. The table arrangement, however, makes 
it much easier to compare results. The table, made out 
in this way, should be placed in the note-book, and as 
the different cases are tried the galvanometer readings 
obtained can be placed where they belong in the last col- 
umn. From the study of the table, which arrangement of 
cells seems to give the most current when the external re- 
sistance is high and which when the external resistance is 
low ? 

Unit of Resistance. — If resistances are to be compared 
accurately, a standard of resistance is needed. As we 
have found that resistance depends on length, cross-section, 
and material, we can get a standard of resistance by taking 
a specified length of a specified body of a specified cross-sec- 
tion. When the body used is mercury, cooled to the freez- 
ing-point of water, the length about 1 meter, and the 
cross-section 1 sq. millimeter, the resistance is said to be 
1 ohm. Any body having a resistance equal to that of the 
standard mercury column is said to have a resistance of 1 
ohm. 

Resistance-box. — The instrument commonly used in 
measuring resistance is called a resistance-box or rheostat. 
It is an arrangement by which different coils of wire of 
known resistance may be placed in the circuit. A com- 
mon form, together with a sign for a diagram, is shown 



40 



CURRENT ELECTRICITY. 



in Fig. 27. It consists of a wooden box provided with 
three switches. A number of metallic heads are placed in 
semicircles about the pivots of the switches. Each head 
is furnished with a number which indicates the resistance 




in the circuit when the end of the switch rests on that 
head. One switch (the one at the right in Fig. 27) places 
from to 1 ohm in the circuit, the second from 1 to 10 
ohms, and the third from 10 to 100 ohms. By using all 
three switches, any resistance from to 111 ohms may 
be placed in the circuit. The sum of the readings of the 
three switches is taken as the measure of the resistance ; 
for example, in the figure the box reads 55.9 ohms. The 
box has two binding-posts for making connections. 



EXERCISE 7. 

RELATIVE RESIST A XCE. 

Preliminary. — In the following experiment we wish to 
find the lengths of iron and copper wire equivalent in re- 
sistance to 1 centimeter of German-silver wire. We must 
place a known length of German-silver wire in the cir- 



RELATIVE RESISTANCE. 



41 



cuit, observe the deflection of the galvanometer, and then 
find the lengths of the wires of other materials required 
to produce the same deflection of the galvanometer. We 
will use the apparatus indicated in Fig. 28. 

The board A carries two uprights, BB, which support a 
meter-stick, M. Stretched between these upright, is a piece 
of uncovered German-silver wire, on which slides a hook 
made of the end of one connecting-wire. Above the Ger- 
man-silver wire the iron and copper wires are stretched 
between the uprights, passing back and forth several times. 
A binding-post, a, is connected with one end of all three 




sets of wires. When the circuit is completed from the 
binding-post a, through the wire and the hook that slides 
on it, the length of wire in the circuit will be determined 
by the length of wire between a and the hook, as read on 
the meter-stick, and can be varied by sliding the hook along 
the wire, so varying the resistance. (Experiment 4, Part 
II.) More than one meter of the wire may be placed in 
circuit by attaching the hook to the wire running back to 
the right-hand upright. The total length of wire in the 
circuit in each case will be the ivhole length which the 
current passes through in going from the binding-post to 
the hook. 



42 



CURRENT ELECTRICITY. 



EXPERIMENT. 

Apparatus.— Cell; rack with wires (Fig. 28); reverser; galvanome- 
ter ; connecting-wires.* 

Object. — To find what length of iron and copper wires 
give a resistance equivalent to that of one centimeter of 
German-silver wire. 

Manipulation. — Having set up the cell and connected 
the galvanometer for ten turns, introduce the German- 
silver wire into the circuit, by attaching one connecting 
wire to the binding-post a and connecting the wire leading 
from the hook with the other element of the cell. The 
distance from the hook to the binding post, as read on the 
meter-stick, gives the length of German-silver wire in the 
circuit. Observe the galvanometer-reading with 50 cm. of 
wire in the circuit, then remove the hook from the German- 
silver wire, place it on the iron wire, and find by trial the 
position which gives the same galvanometer-reading. Re- 
peat the operation with the copper wire, recording the total 
lengths in circuit in each case. Now, starting with 40 cm. 
of German -silver wire, again find corresponding lengths 
of iron and copper wire. Try some other lengths if time 
allows. Tabulate results as follows : 



G. S. wire. 


Galv.-read. 


Iron wire. 


Copper wire. 


Iron wire 
equal to 
1 cm. G.-S. 


Copper wire 

equal to 
1 cm. G.-S. 




R. 


L. 


Av. 











EXERCISE 8, A. 

MEASUREMENT OF RESISTANCE. 

Preliminary. — The purpose of the following exercise is 
to determine the resistance of a body by what is called the 
"method of substitution." This method is based upon 
* Qne with hook, or au "English" binding-post. 



MEASUREMENT OF RESISTANCE. 



43 



the fact that bodies of equal resistance introduced into the 
same circuit will transmit the same amount of current. 
We find the resistance in ohms of a body which will 
transmit the same amount of current transmitted by a 
body of unknown resistance.* The apparatus used is as 
shown in Fig. 29. A galvanometer, G, a resistance-box, R, 
and mercury-cups, mm, are connected in the circuits of a 



c 


~\ 




b\ 




\i 


y ' 






R 




U 






m 


m 





cell, B. The mercury-cups afford a means of easily insert- 
ing a body into the circuit. On replacing the body by a 
piece of thick copper wire the resistance of the mercury 
cups is practically reduced to 0, which is equivalent to 
taking them out of the circuit. By setting the switches 
of the resistance-box at 0, that also is practically taken out 
of the circuit, so that it is not necessary to disconnect it 
when the current is passed through the body. 

EXPERIMENT. 

Apparatus.— Cell; resistance-box; galvanometer; connecting- wire; 
conductor whose resistances are to be measured; mercury-cups; 
reverser. 

Object. — To determine the resistance of a body in ohms 
by the method of substitution. 



* Let the pupil prepare a statement of the conditions necessary for 
carrying out such an experiment. 



44 



CURRENT ELECTRICITY. 



Manipulation. — Having all three switches of the re- 
sistance-box on the zero-point (that is, having no resist- 
ance in the box), connect the mercury-cups by each, in turn, 
of the coils of wire whose resistance is required, and read 
the galvanometer.* Replace the coil by the short piece of 
copper wire (so that the mercury-cups offer practically no 
resistance), bring your eye directly over the galvanometer- 
needle, and, without looking at the box, turn the 10-ohm 
switch until the galvanometer reads as close to the former 
reading as you can get, that is, until the addition of an- 
other 10 ohms makes it too low. Adjust now the ohm 
switch in the same manner, and lastly the 0. 10-ohm switch. 
The adjustment of the switches should be done with the 
right hand, the eye being kept constantly on the needle. 
Read the resistance in the box. This is equal to the re- 
quired resistance of the coil of wire. Repeat with the 
same coil, being careful not to look at the box so that your 
second trial may not be biased by the results of the first. 
Determine in this way the resistance of several coils of 
wire. Record as follows : 



Length. 


Material. 


Galv. -reading. 


Resistance. 


No. of Wire. 


R. 


L. 


Av. 

















* As all that is needed is to get the same galvanometer-reading, it 
is not necessary to reverse the galvanometer. In this case, however, 
all deflections must be on the same side. The first and second read- 
ings should be taken in as rapid succession as possible, in order to 
decrease the effect of any possible change in the current. 



MEASUREMENT OF RESISTANCE. 



45 



EXERCISE 8, B. 

MEASUREMENT OF RESISTANCE. 

Preliminary. — When, in such an apparatus as Fig. 30 rep- 
resents, the current of the battery B comes to the point a, 
it divides, part going down the side abd and part down the 
side accl. If the resistances of the two sides are alike, the 
same amount of current will flow through each; but if they 
are not alike, more current will follow the side having the 
less resistance. If w T e attach wires at the points b and c 
and connect them with the galvanometer, so long as the 
same amount of current passes on each side the galvanome- 
ter will not be affected; but if the resistance of one side 




be made greater than that of the other, then the current 
will flow through the galvanometer from the side carrying 
the greater current. Suppose we insert in cd a resistance- 
box, and in bd the body whose resistance we wish to meas- 
ure, x. If the resistance-box is at 0, the resistance of x 
will hold back the current in bd, and a portion of it will 
flow from b to c through the galvanometer, which will be 
deflected. Suppose now we increase the resistance in the 
box until the galvanometer reads 0, then we know that the 
resistance of acd equals the resistance of abd (since the 
wires of which the instrument are constructed have practi- 



46 



CURRENT ELECTRICITY. 



cally no resistance), and that the required resistance of x 
equals the known resistance in the box. 

Wheatstone's Bridge. — On a board is placed a square of 
wire, abed, Fig. 31, with a binding-post at each corner. 

B 




The sides M and dc are cut, and two binding-posts inserted 
in each. From the binding-posts b and c wires (dotted 
lines) are led to the galvanometer G, and the battery-wires 
are attached to the binding-posts a and d. In the battery- 




circuit is placed a key, K, which closes the circuit when 
depressed. A similar key, K' , is placed in the galvanom- 
eter-circuit. The substance to be tested, x, is attached 



MEASUREMENT OF RESISTANCE. 47 

to the binding-posts gh, and the resistance-box, R, is con- 
nected at ef. Fig. 32 is a picture of the same apparatus 
when ready for use. 

EXPERIMENT. 

Apparatus.— Wheatstone's Bridge; cell; galvanometer; two con- 
tact-keys; resistance-box; bodies whose resistances are to be meas- 
ured; bar-magnet; connecting- wires. 

Object. — To determine the resistance of a body by the 
use of Wheatstone's Bridge. 

Manipulation". — Connect the binding-posts gh, Fig. 31, 
by the substance whose resistance is required. Close the 
battery-circuit. Then close the galvanometer-circuit for 
an instant only, and observe the direction of the " throw" 
of the galvanometer-needle. Add resistances, observing 
the throw of the galvanometer-needle- after each addition, 
until it begins to move the other way. Then work down 
with the resistance-box until, on closing both circuits, no 
tremble of the needle is observed. The resistance in the 
box is then equal to the unknown resistance. 

Precautions. — 1. Avoid throwing the galvanometer- 
needle violently. This may be avoided by closing the gal- 
vanometer-circuit only for an instant until there are such 
resistances in the box that the galvanometer-needle scarcely 
moves. A longer contact is then safe. 2. Always close 
the battery-circuit before closing the galvanometer-circuit. 
3. Be sure that all contacts are good. 

During the first part of the experiment the motion of 
the needle may be very much deadened by placing a bar- 
magnet due north of the needle, in a north and south line, 
with its south pole near the north pole of the needle. 
During the latter part of the experiment the magnet may 
be removed. The presence of the magnet also tends to 
prevent the needle from oscillating, and saves time lost in 
waiting for the needle to come to rest after each trial. 



48 CURRENT ELECTRICITY. 

EXERCISE 9. 

ELECTRO-MOTIVE FORCE. 

Preliminary. — We have observed that bodies differ from 
one another in resistance to an electric current, and have 
also noted the conditions upon which this resistance de- 
pends. Suppose, now, we place the same body in various 
circuits, will it always transmit the same amount of cur- 
rent ? That is, have all currents the same power of over- 
coming a given resistance? Let us see if the conditions 
under which the current is generated make any difference. 
For this purpose try plates of various materials in the cell, 
being careful that they are the same size and distance 
apart, and that the external circuit is the same. With a 
galvanometer connected, we can see if the currents gener- 
ated all have the same power of overcoming resistance. 

EXPERIMENT. 

Apparatus.— Tumbler-cell; plates of iron, lead, copper, with 
leading-wires; galvanometer; reverser. 

Object. — (1) To see if all currents have the same power 
of overcoming resistance. (2) To study the conditions af- 
fecting this power. 

Manipulation. — Lay one of the plates on the table, put 
on it two little pieces of wood, lay the other plate on them, 
slip a rubber band around the whole, and place in the 
liquid in the tumbler. Connect the galvanometer, ad- 
justed for ten turns, close the circuit, and read the galva- 
nometer. If a reverser is available, use it ; if not, reverse 
by changing connections. Try the cases given in the fol- 
lowing table, and any others that you can. 

The plates in each case being the same size and distance 
apart, and the external circuit the same, the resistance is 
practically alike in each trial. From the study of the re- 



ELECTROMOTIVE FORGE. 



49 







Galv. -reading. 


Positive Plate. 


Negative Plate. 




R. 


L. 


Av. 


Copper 


Carbon 








Carbon 


Zinc 
Iron 








Iron 


Lead 








Carbon 


" 








Lead 


Zinc 








Carbon 


Carbon 








Zinc 


Zinc 








Copper 


Iron 
Lead 
Copper 









suits obtained, what do you infer regarding (1) the power 
of different currents to overcome resistance, and (2) the 
conditions affecting this power? 

Questions. — Why are zinc and carbon usually used 
in galvanic cells ? Would zinc and copper do as well ? 
Why not use iron ? What conditions seem to affect the 
results observed? 

Supplementary. — The power possessed by a current of 
overcoming, or the power that pushes the current through 
the resistance, is said to be due to the Electro-motive Force 
(often written, for brevity, E. M. F.). The higher the 
E. M. F., the more current will pass through a given re- 
sistance, and the lower the E. M. F., the less current will 
pass through the same resistance. In a general way, the 
idea of electro-motive force corresponds to the " head " of 
water in a pipe; that is, to the pressure which pushes the 
water through the pipe. The higher the pressure, the 
more water will pass through the pipe; and the lower the 
pressure, the less will pass through the same pipe. 

In the measurement of E. M. F., the standard is very 
nearly that given by a gravity-cell (zinc and copper in 
solutions of blue and white vitriol). The amount of cur- 



50 CURRENT ELECTRICITY. 

rent generated by the cell under test that will pass through 
a resistance is measured and compared with the amount 
that passes when a standard cell is used. 

Questions. — 1. Which gives the greater E. M. F., car- 
bon and zinc, or iron and zinc ? 2. What E. M. F. is pro- 
duced by two like plates ? 3. What seems to determine 
the E. M. F. in a galvanic cell? 

EXERCISE 10. 

ELECTRO-MAGNETISM. 
EXPERIMENT 1. 

Apparatus.— Carriage-bolt ; 100 cm. No. 18 wire ; cell ; compass ; 
iron-filings ; paper and pencil ; current; some means of varying 
resistance of the circuit and of reversing the current. 

Object. — To study the magnetic effects of an electric 
current and the conditions affecting the strength of an 
electro-magnet. 

Manipulation. — Part I. Hold the carriage-bolt in 
front of you with the nut away from you and wind around 
it 15 or 20 turns of insulated wire from left to right (if a 
watch were facing you, the turns would be with the direc- 
tion of the motion of the hands). Arrange as in Fig. 33. 




Complete the circuit. Note what happens. Test the 
other end at the compass. Move the compass along from 
one end of the bolt to the other. Note what happens to a 
piece of soft iron when a wire carrying a current is coiled 
around it. 

Part II. Kepeat Part I with the current reversed. 



ELECTRO-MAGNETISM. 51 

Part III. Kewind the wire in the opposite direction, 
repeat Part I, and observe the result. 

Part IV. Eeverse the current, and again repeat. 

Questions. — 1. What is the effect of reversing the cur- 
rent ? 2. What effect has the direction of the current ? 
3. What happens when the circuit is broken ? Does the 
effect produced by the direction of the current entirely 
disappear when the circuit is broken ? 

EXPERIMENT 2. 

Object. — To see if an electro - m agnet * resembles an 
ordinary magnet. 

Manipulation. — Bring the electro-magnet up to some 
iron-filings, and see if it attracts them. 

EXPERIMENT 3. 

Object. — To investigate the conditions affecting the 
power of an electro-magnet. 

Manipulation. — Lay a sheet of paper on the table, 
place the electro-magnet on it, and draw a pencil-line 
around the magnet so as to mark its position on the 
paper, f Place the compass about east of one pole of the 
electro-magnet, and at such a distance that when the cur- 
rent is turned on the magnet pulls the compass-needle 
around 15 or 20 degrees. Mark this position also. 
Change the current by varying the resistance in the 
circuit. Has the strength of the current any effect on the 
strength of the magnet? Put as many more turns on the 
magnet as you have already. Observe the results. J What 
effect has the number of turns ? Give diagrams. 

* A piece of iron magnetized as in Exp. 1, by an electric current, 
is called an electro-magnet. 

f This precaution is taken in order that the distance from the 
magnet to the compass may be kept the same. Of course, for each 
test, both magnet and compass must be on the marks. 

X In comparing the effects of different numbers of turns, the same 
Current should be used. 



52 



CURRENT ELECTRICITY. 



Questions. — 1. What must be done in order to obtain 
an electro-magnet ? 2. What determines the nature of 
the poles ? 3. What determines the strength of the mag- 
net? 



EXERCISE 11. 

INDUCED CURRENTS. 

Preliminary. — Arrange the apparatus as in Fig. 34, 

+ 




where the electro-magnet, A, is placed in the circuit, into 
which is also introduced the reverser, R. The ends of the 
coil of a second electro-magnet, B, are connected by 
flexible wires with the sensitive galvanometer, G. 

When the current passes around A it becomes a magnet, 
and, if B is placed upon it, B becomes an induced mag- 
net. Hence when the current is sent into A the result is 
equivalent to thrusting a magnet suddenly into the coil B, 
whose ends are connected with the galvanometer. By 
means of the reverser, the poles of A may be suddenly 
changed, and the same effect produced as if the magnet 
in B were suddenly withdrawn, turned end for end, and 
replaced in the coil. Slowly separate A and B and the 
effect is equivalent to slowly withdrawing the magnet from 
the coil B. Bring them slowly together, and the opposite 
effect is produced, 



INDUCED CURRENTS. 53 

EXPERIMENT 1. 

Apparatus.— Two electro-magnets; a strong current; connecting- 
wires; galvanometer; reverser; means of making and breaking the 
circuit, and, if possible, some means of varying current strength; 
clamp to suspend one coil. 

Object. — To observe the results of suddenly thrusting a 
magnet into a coil of wire. 

Manipulation".— Place B upon A. When the galva- 
nometer-needle is at rest, suddenly close the circuit of A 
(that is, suddenly introduce a magnet into B). Observe 
and record carefully the behavior of the needle. 

EXPERIMENT 2. 

Object. — To observe the effect of withdrawing the mag- 
net from the coil. 

Manipulation. — While the current is passing through 
A and the galvanometer-needle is at rest, break the circuit 
of A. Observe and record as above, 

EXPERIMENT 3. 

Object. — To investigate the effect of the nature of the 
pole used. 

Manipulation. — Change the reverser and turn on the 
current in A. The poles of A, and hence those of the 
induced magnet in B, will be reversed. Observe results. 

EXPERIMENT 4. 

Object. — To observe the effect of moving a coil of wire 
with an iron core in the field of a magnet. 

Manipulation. — Remove the coil B from A. Close 
the circuit of A, and then move B up to and away from A, 
in various directions and with various speeds. Observe 
the galvanometer indications carefully in each case, with a 
view to stating the conditions affecting the amount of cur- 
rent, its direction, etc. If practicable, change the strength 
of the current through A to see if the strength of the 



54 CURRENT ELECTRICITY. 

magnetic field makes any difference. Tabulate results as 
follows : 



How B was moved. 


Direction of 
Galvanometer-reading:. 


Amount of Galv.- 
reading. 









In the first column insert the words "towards A," "away 
from A" "in a horizontal circle above A" as the case 
may be. In the second column insert the words " right " 
or "left," as the case may be. In the third column, the 
words " more," " less," etc. 

Questions. — 1. Is it possible to obtain electricity by the 
use of magnets ? 2. What conditions have you found to 
be necessary ? 3. What conditions have you observed to 
affect the amount of the current,* and its direction? 
4. Would it be possible to construct a machine on this 
principle which could be used to produce a current of 
electricity? 5. What would be the essential parts of such 
a machine ? 

A mechanical contrivance for fulfilling these conditions, 
and thus generating electricity from motion, is called a 
Dynamo-electric Machine, or simply a Dynamo. 

EXPERIMENT 5. 

Object. — To see if, reversing the last process, motion 
can be obtained from a current. 

Manipulation. — Set up the apparatus as in Fig. 35. 
Having a arranged as in Exp. 4, suspend b above it, and 
disconnecting the wires from the galvanometer, connect 

* Notice that as the resistance of the galvanometer coil B and 
the connecting-wires is always the same, any changes in the amount 
of current observed must be due to changes in the E. M. F. of the 
induced current ; hence the conditions that seem to determine the 
amount of the current are really those which determine the E. M. F. 



INDUCED CURRENTS. 



55 



them with the circuit as shown, the reverser being in 
circuit with the lower magnet and b being suspended a 
little to one side of a.* Close the circuit through b and 
then through a, and notice the results. Suddenly reverse 




the current through a, and see if by reversing at the 
right time you can keep b swinging. A bar-magnet 
arranged as in Exp. 8 may be useful. 

Questions. — 1. Is it possible to obtain motion from an 
electric current? 2. Would it be possible to construct a 
machine on this principle which could be used to produce 
motion from an electric current? 3. What would be the 
essential parts of such a machine ? 

A mechanical device for fulfilling these conditions and 
thus obtaining motion from electricity is called an Electric 
Motor. 

* Two cells may be used, or the two coils may be placed in paral- 
lel on one circuit. 



MENSUEATION. 
NOTES ON MEASUREMENT. 

Units of Measure. — If we wish to know just how many 
times one body is larger than another, that is, if we wish 
to make an exact comparison between the two bodies, we 
must ascertain the value of each one in terms of some 
fixed standard of measurement. Thus, to compare exactly 
the lengths of two boards, as a preliminary we refer both 
lengths to a fixed standard of length, and find out how 
many times this standard is contained in each of the 
lengths. Or, again, suppose we wish to compare the 
lengths of the two lines AB and CD, Fig. 36. Let us 



c d 

Fig. 36. 

call the short line cd the standard. We find that AB is 
equal to 10 times cd and CD = 7 cd. Then we know that 
the lengths of AB and CD are as 10 to 7. In case cd is 
not contained an integral number of times in AB and CD, 
it must be divided into known fractional parts, and the 
lengths expressed as so many cd's plus so many fractions of 
cd. In the same way, if we wish to compare volumes, a 
standard volume must be employed. Thus we can find 

56 



NOTES ON MEASUREMENT. 



57 



how many times the little cube, abcdef, Fig. 37, is con- 
tained in the two larger cubes. If it is contained 36 times 
in one and 8 times in another, we say the volumes of the 
larger cubes are as 8 to 36. As a standard in comparing 



71 (- 



values we refer to dollars; in lengths, we refer to feet, 
meters, or miles; in volumes, we refer to quarts, gallons, 
or cubic inches, etc. Such a standard is called a Unit. 

English and French Systems. — Of course any length or 
volume could be used as a unit, but in practice those 
adopted by the government or by custom are employed. 
Measurements of length, breadth, or thickness are called 
Linear Measurements. The common standard of length 
is the yard, which was originally adopted by the English 
Government as the length of a certain metal rod in their 
possession, and has been accepted by our own Government. 
The smaller units are the foot (one third of a yard), and the 
inch (one thirty-sixth of a yard, or one twelfth of a foot). 
These are called the English units, and in using them we 
are said to use English Measure. The inch is commonly 
divided into halves, fourths, eighths, sixteenths, etc. In 
scientific work, however, fractions of an inch are expressed 
as decimals. We also use the French or Metric System. 
Its standard is the length of a certain rod, called a Meter, 



^ 



58 MENSURATION. 

which is in the possession of the French Government. 
This is divided into 100 equal parts, called centimeters, 
and into 1000 parts, called millimeters. Thus a centi- 
meter equals 10 millimeters. These prefixes, cent and 
mill, and their meanings, are familiar in our money. 

Dollar. Meter. 1. 

Cent. Ce dimeter. T ^. 

Mill. Millimeter. tttoo- 

This system has the advantage of being divided decimally, 

so that a change from one unit to another can be effected 

by moving the decimal-point. 

As a unit of Surface, we use a surface equal to that of a 
square measuring a unit of length on each side. Thus we 
have a square yard, square meter, etc. Such measure is 
called Surface or Square Measure. The surface expressed 
in square measure is the Area. 

For comparing volumes, we use a volume equal to that 
of a cube, measuring a unit of length on each edge. Thus 
we have a cubic foot, cubic meter, etc. The unit used in 
our experimental work is generally the cubic centimeter, 
and sometimes 1000 cu. cm. or a liter. We have also 
quarts, gallons, etc., these quantities being the volumes of 
certain vessels belonging to the Government. 

Change from one System to the Other. — If we know the 

value of one unit in terms of another, we can change from 

one system to another. The meter is 39.37 inches long. 

Suppose we wish to express 26 meters in yards. If one 

meter = 39.37 in., 26 meters = 26 X 39.37, or 1023.62 in., 

1023.62 
and as one yard — 36 in., — — r — = number of yards 

= 28.85. Again, let us change 15 yards to meters. 15 
yds. = 15 X 36 in. = 540 in. If one meter = 39.37 in., 
there will be as many meters in 540 in. as 39.37 is con- 
tained in 540, or 13.7 meters. Another method is as fol- 



DETERMINATION OF LENGTH. 59 

lows: One } T ard = 36 in., one meter = 39.37; then a yard 

== ww^^ of a meter, and a meter = — ^— - of a yard. If 
39. o< 36 

we change these fractions to decimals, we get 1 yard 

36 39 37 

s= oft ~ meters, = 0.9144meter; 1 meter = ' = 1.0936 
Sv.oi do 

yds. Then if 1 meter = 1.0936 yards, 26 meters will 

equal 26 X 1.0936 yds., or 28.85. Similarly, if 1 yd. 

= 0.9144 meter, 15 yds. = 15 X 0.9144 = 13.7 meters. 

Abbreviations. — Meter, m. ; centimeter, cm. ; millimeter, 
mm. ; liter, 1. ; cubic centimeter, cu. cm. 

It must be remembered that in surface measurement 
the units go by the square of 10, and in cubic measure by 
the cube of 10. Thus there are 100 2 or 10,000 sq. cm. in 
1 sq. m., and 100 3 or 1,000,000 cu. cm. in a cu. m. 

DETERMINATION OF LENGTH. 

Scales. — The English Scale gives results in inches, and 
is shown as commonly arranged in Fig. 38. The long 
numbered lines 
mark inches; the 
shorter lines, half- 
inches ; the still 
shorter, quarter - 
inches ; and the 
shortest, eighths. fig. 38. 

The results are here expressed in inches and decimals of 
an inch, not in vulgar fractions; as 0.125, instead of j, 
or 2.375 in. for 2f in. Yard-sticks are used in laboratories.* 

The usual form of the Metric Scale is shown in Fig. 39. 
The long lines, as act, mark decimeters; the shorter num- 
bered lines, as bb, centimeters; the still shorter, cc, 0.5 cm., 
or 5 millimeters; the shortest lines, millimeters. Readings 

*In some forms of meter-slicks there is an inch-scale on one side. 
Do not use these for yard-sticks. 




60 



MENSURATION. 



are usually expressed in centimeters and decimals of a cen- 
timeter. For example, the scale to the line A B reads, in 
Fig. 39 (from right to left), 59 cm. plus 3 mm.; this would 
be recorded 59.30 cm. Meters are 
used for distances of over 100 cm. 
When the figures on scales are right 
side up, the scale reads from right to 
left. This must be remembered or 
mistakes will happen, as it is natural 
to try to read from left to right. 
Tenths of millimeters should be esti- 
mated by the eye. 

Reading Scales. — The scales are car- 
ried out to the edge of the rod (Figs. 
40 and 41), and when possible this 
edge should be placed against the dis- 
tance to be measured, as in Fig. 40, 
where it is desired to measure the dis- 
tance between the lines aa. Where 
the scale cannot be applied directly to 
the object, be sure that the line of sight 
is always perpendicular to the scale. 
A metric scale should be read to T \ 
mm., the fraction of a millimeter di- 
vision being estimated by the eye. In 
general, an attempt should be made 
to read a scale to a fraction of the 
smallest division. 

When determining shorter distances 
than the length of the measuring rod, 
where the body is loose and can be brought directly 
against the scale, it is not best to start at one end of the 
rod, but rather to bring the body to be measured near 
the middle of the rod, place one point on a numbered 
line (in a metric scale one of the decimeter lines), and 



E-°9 



DETERMINATION OF LENGTH. 



61 



read the position of each point on the scale. Suppose, 
for example, it is desired to measure the length of the box 
A BCD in Fig. 41. Lay the scale down on top as in the 
the diagram, and read the positions of A and B. Say 
A = 26.14 cm., B = 42.81 cm., then B — A = 42.81 - 
26.14, or 16.67 cm. 




llillllllllllllllllllllllllll 




Suppose, again, the diameter of a sphere is needed. 
Obtain two rectangular blocks, aa in Fig. 42, and place 
the sphere between them, the whole resting on a level 
surface. Bring the blocks up against the sphere with their 
faces parallel. Then the distance between the blocks is the 
diameter of the sphere. Measure from edge to edge di- 



.-1 . 1 'ill lilil « h Ii1.li 1 1 -I ■ I ■ hi ill li 




.1.1,1.1. 




B A 
C 


D 

/ 





rectly over the centre of the sphere. The ball should be 
turned and the work repeated a few times. Both blocks 
should be set against a smooth vertical surface. In all 
these cases the same precaution is necessary, — to have the 
line of sight at right angles to the surface on which the 
scale is marked. 



62 



MENSURATION. 




When the scale cannot be brought up to the body, special 
methods are resorted to. One is called The Compass 
Method. A pair of compasses or dividers are adjusted 
until the distance between 
their points is just that to 
be measured. The compasses 
are then applied to the scale, 
with one point on a num- 
bered line, and the position 
FlG - 42 - of the other point is read. 

Sometimes a pointer is to be read against a scale, as in 
getting the Coefficient of Expansion. Always have the 
pointer as near the scale as possible, but not touching it, 
and arranged so that in moving it along the scale it is the 
same distance from it. Always read from the same side of 
the pointer. Best of all, end the pointer with a fine needle, 
and have the point of the needle read on the scale. A 
magnifying-glass is often of assistance. 



EXERCISE 1. 

PRACTICE IN THE USE OF LINEAR SCALES. 
EXPERIMENT. 

Apparatus.— A sheet of paper on which two crosses have been 
ruled with a sharp pencil, 30 or 40 cm. apart; a meter-stick with 
English scale on one side (or a meter-stick and a yard-stick). 

Object. — To determine: (a) The distance between the 
centres of the two crosses in inches, (b) The same distance 
in centimeters, (c) From these data,* the number of 
inches in a meter. 

Manipulation. — Lay the sheet of paper smoothly upon 
the table, place the metric scale upon it, bring the centres 
of both crosses to the edge of the scale, and record their 

*This word means the numerical results of the experiment, which 
are afterwards used in the calculation. 



PRACTICE IN THE USE OF LINE AH SCALES. 63 

readings. Read the scale to 0.1 mm., observing all the pre- 
cautions given in the ' ' Notes on Measurement." Try five 
times, using different parts of the scale each time. Record 
results as in the following example, which gives the actual 
data of one set of determinations with this apparatus: 

TABLE I.— METRIC MEASURE. 



No. of Trial. 


Reading L. H. Point. 


Reading R. H. Point. 


Length in Cm. 


1 
2 
3 
4 
5 


72.81 cm. 
82.80 " 
51.79 " 
61.30 " 
30.79 " 


50.00 cm. 
60.00 " 
29.00 " 
38.50 " 
8.00 " 


22.81 
22.80 
22.79 
22.80 
22.79 



Average length in cm., 22.79 cm. 

With the same precations, measure the distance between 
the centres of the crosses in the English system, reading to 
one-sixteenth (0.0625) inch, mentally changing the fractions 
of an inch to decimals. Arrange the results as follows : 

TABLE II.— ENGLISH MEASURE. 



No. of Trials. 


Reading L. H. Point. 


Reading R. H. Point. 


Length in Inches. 


1 
2 
3 
4 
5 


1 inch. 
5 inches. 

7 " 
10 " 
13 " 


9.937 inches. 
13.975 " 
15.959 " 
18.968 " 
21.975 " 


8.937 
8.975 
8.959 
8.968 

8.975 



Average length in inches, 8.963 inches. 

Calculation. — Having now the values of the same dis- 
tance in centimeters and in inches, the number of centi- 
meters to the inch can be found by the following calcula- 
tion: 

Number of cms. : 100 cms. : : number of inches : x. 
x ~ number of inches in 100 cms. (1 meter). 



64 



MENSURATION. 



Taking the data given above : 

22.79 cms. : 100 cms. :: 8.9G3 inches : x 
100 X 8.963 



22.79 



= 39.31, 



which would be the value given by these data for the num- 
ber of inches in the meter.* 



EXERCISE 2. 

THE RELATION OF CIRCUMFERENCE TO DIAMETER. 

EXPERIMENT. 

Apparatus.— Meter-stick (English and French scales), card-board 
circles, 10 cm., 20 cm., and 30 cm. in diameter; pencil; strip of paper 
or card-board about 1 m. long. 

Object. — To obtain answers to the following questions : 
(1) Is there any definite relation between the diameter of 
a circle and its circumference ? (2) Do these results hold 
true for more than one method of measurement ? (3) Is 
this relation the same for circles of different diameters ? 
(4) Given the diameter of a circle, can the circumference 
be found ? If so, how ? (5) Given the circumference of 
a circle, can the diameter be found ? If so, how ?f 

Manipulation. — Method A. Make a pencil-mark on 
the edge of the circular disk of paper (Fig. 43). Roll the 

disk along a straight 
line ruled on a piece 
of paper tacked to the 
table, starting with the 
FlG 43 - pencil-mark just on the 

line, and rolling until the mark just touches the line again. 






* These data give a value a little below the true one, viz., 39.37. 
f As in all experimental work, first lay out a general method. In 
this case the general method is,— to answer question 1, measure the 



RELATION OF CIRCUMFERENCE TO DIAMETER. 65 

Carefully measure the distance on the line between the 
two points touched by the pencil-mark. This gives you 
the circumference. 

Method B. Lay the measuring-rod on the table and roll 
the disk along it, as in Fig. 44. This gives the required 



^ 



length directly on the rod. To measure the diameter, lay 
the disk flat on the table and measure the distance across 
it at its widest part. Make each measurement both in 
centimetres and inches; repeat three times, and record the 
results each time. The three numbers obtained for the 
circumference will not be just the same, owing to errors in 
manipulation, reading, etc. Add them, and divide the 
sum by the number of measurements. This gives the 
average measurement of the circumference.* Do the same 
for the diameter measurements. Then divide the average 
circumference by the average diameter. This gives a num- 
ber which, except for errors, is that by which the diameter 
must be multiplied to obtain the circumference. It should 
be a little over three, and should be carried out to four 
decimal places. Do the same for the measurements in 
inches, and compare the numbers obtained in the two 



circumference and diameter of a circle and find if any relation 
exists between them ; to answer questions 4 and 5, use the knowl- 
edge obtained in answering question 1 ; to answer question 2, com- 
pare results obtained \>y using different methods of measurement ; 
to answer question 3, use circles of different sizes. 

* Of course this is to be done separately for the measurements in 
inches and in centimeters. 



m 



MENSURATION. 



cases. Arrange in the note-book a table of results as 
follows : 



CIRCLE I. 
Measured in centimeters. Method k ' A. ' 



Circum. 


Diam. 


Av. Circum. 


Av. Diam. 


Av. Circum. 


Av. Diam. 













CIRCLE I. 
Measured in inches. Method " B.' 1 



Circum. 


Diam. 


Av. Circum. 


Av. Diam. 


Av. Circum. 


Av. Diam. 













Repeat in exactly the same way with Circle II. Answer 
in order the questions given above, and also state which 
method in your opinion yields the best results, and why ? 

Calculation. — There have now been obtained at least 
four values for the number which stands for the numerical 
relation between diameter and circumference. Average 
them, and the result should be nearly correct. Using this 
number, solve the following: 

Problems. — 1. A circle has a diameter of 6 cm.; find 
the circumference. 2. If the circumference is 25 cm., 
find the diameter. 3. If the diameter is 6 inches, find the 
circumference. 4. If the circumference is 25 inches, find 
the diameter. The number is represented in geometry by 
the sign n (pronounced " pi "). Then, with this sign, using 
D as the symbol for the diameter and C for the circumfer- 
ence, express as an algebraic equation the rule for solving 
such problems as the above. 



DETERMINATION OF VOLUMES. 



67 



DETERMINATION OF VOLUMES. 

The Graduate Cylinder. — There are two kinds of meas- 
uring vessels in use for fluids — those measuring only a fixed 



quantity and those meas^ 
uring varying quantities. 
Of the latter kind, the 
two commonly used in 
laboratory work are grad- 
uated cylinders and bu- 
rettes. The graduated 
cylinder, often called 
simply a graduate, is a 
glass cylinder furnished 
with a foot so as to stand 
upright, and with a scale 
for reading volumes, usu- 
ally in cubic centimeters. 
The scale is engraved on 
the glass, and arranged as 
in Fig. 45. There is a 
long numbered line for 
every 10 cu. cm., as a a. 
Between these are shorter 
lines, marking cubic centi- 
meters, as c c; and between 
these, in turn, still shorter 
ones, marking half cu. cm. 
Such a scale is said to read 
to 0.5 c.c. There are usu- 
ally two scales, one having! J 

the at the top and the fig. 45. 

other at the bottom, the former used in measuring the 
volumes of liquids poured out of the cylinder, the latter 
in measuring the volumes of liquids poured in. 



68 



MENSURATION. 



On looking horizontally at a graduate containing a 
liquid, the surface of the liquid appears as a dark band, 




usually curving down in the centre, as in Fig. 46. This 
curve is called the meniscus, and the line correspond- 
ing to the lowest point of the meniscus is taken as the 
level of the liquid. The cylinder must be placed on a 
firm horizontal surface, and the eye brought to the level 
of the meniscus and directly opposite the scale. In Fig. 
47 a represents the correct method of reading, b and c 
the incorrect, b would give a reading greater and c less 
than the true one. Errors caused by failure to read a 
scale with the lrne of sight in the proper position are said 
to be due to Parallax. The following method will avoid 
such errors: 

Take a piece of stiff paper about 1J X 4 inches, being 
sure that the upper edge is clean and straight. Wrap' it 
around the cylinder, and allow a portion to project, as 
shown in Fig. 48. Grasp the projecting portion with the 
finger and thumb, taking care that the upper and lower 



DETERMINATION OF VOLUMES. 



are even with each other. Draw the paper tightly 
around the cylinder, and move it until, on sighting across 
the top edge from one side to the other, the meniscus just 




touches it; Fig. 49. In this position the "sight" is horizontal. 
If the upper edge of the paper is just on a line of the 
scale, this gives the reading ; but if not, the fraction must 
be estimated by the eye and expressed as a decimal. Sup- 
pose it comes, as in Fig. 50, between the 17 and 18 line. If 
half-way between, read 17.5 ; if one third the way, 17.33 ; 
if two thirds, 17.66 ; if three fourths, 17.75; etc. On the 
graduates commonly used remember that the space between 
two lines is half a cubic centimeter. Hence, if half-way, 
read 0.25 ; if one fourth above, 0.12 cu. cm.; etc. As a 



70 



MENSURATION. 



rule, any scale can be read to one tenth of its smallest 
division. When there is occasion to read mercury in a 




tube or graduate, it will be found that the meniscus is re- 
versed (Fig. 51), curving up in the centre instead of down. 
In this case always read the level of the top of the menis- 
cus, which can be done by the method just described. 

When measuring out from a cylinder, it is generally 
best to fill it first to the mark; though of course the 
level of the liquid can be read anywhere on the scale, and 
then read again after pouring off; the difference in the 
readings giving the volume poured off. In pouring from a 
cylinder, spilling can be avoided by holding one end of 
a glass rod against the lip of the jar, and the other end 



DETERMINATION OF VOLUMES. 



71 



against the inside of the receiving vessel, as in Fig. 52. The 
liquid will follow the rod. On righting the cylinder 





always wait a moment before reading the volume, so that 
the water which has collected on the sides may run back 
again. 

The Burette. — This is a long narrow tube having a scale 
on one side. (See Fig. 53.) A rubber tube is drawn over 
the lower end, which is narrowed, and the tube is provided 
with a spring clamp, a, which pinches the sides together. 
On pressing the ends of the clamp the rubber tube is 
allowed to expand and the liquid runs out at C at a rate 
proportioned to the pressure on the clamp. A burette is 
filled from the top and usually supported in a vertical posi- 
tion by a clamp. Burettes are usually graduated as in Fig. 
54, which shows a portion of the scale. The long lines 
mark cu. cm. Each space between the cu. cm. lines is 
divided into five parts. Thus the scale reads to one fifth 
(0.2) cu. cm. The lines are numbered at every two cubic 
centimeters. In estimating fractions, one half a space 
= 0.1 cu. cm., one third = 0.06, two thirds = 0.12 cu. cm., 
etc. The scale may be read with a piece of paper like a 
graduated cylinder. 



72 MENSURATION. 

Many burettes are provided with a float, consisting of 
a bulb of glass shaped as in Fig. 55, with a little mercury 
in the lower end so that it will float upright. A line is 
ruled around it (a in Fig. 55). When the float is placed in 
the burette it floats in the liquid, rising and falling with 
it, and the line is observed on the scale through the glass. 
The position of the line is read as the level of the liquid. 
As the float is of nearly the same diameter as the inside of 
the burette (thus bringing the line Very near the scale), 
with ordinary care there is little danger of error due to 
parallax. It is well to tap the burette gently before read- 
ing, as the float is apt to stick a little to its sides. When 
filling the burette, pour the liquid in until the line mark- 
ing its level is above the mark, which is near the top of 
the scale, and carefully draw out the excess until the read- 
ing is 0, allowing the waste liquid to run into a vessel pro- 
vided for the purpose. To make sure that no air remains 
in the rubber tube, fill the burette part full, place the 
upper end in the mouth, and, holding the clamp open, 
blow the liquid nearly out. This repeated several times 
will generally drive out the air. 

Instead of a clamp, burettes are sometimes provided with 
the arrangement shown in Fig. 56. A piece of glass rod 
about a fourth of an inch long, whose diameter is such 
that it will fit tightly in the rubber tube, is cut off, and the 
ends are rounded by heating. The little plug thus formed 
is thrust about half-way up the tube. By pinching with 
the forefinger and thumb on one side of the tube at the 
point where the plug is situated, a channel is formed 
through which the liquid can pass. The rate at which the 
liquid flows depends upon the amount of the pressure. 

Graduated Flask. — This is a vessel having a mark en- 
graved upon its neck. When filled so that the lower end 
of the meniscus just touches the mark, the fla.sk holds a 
fixed quantity of liquid. Those commonly used hold I 



DETERMINATION OF VOLUMES. 



73 



Fig. 53, 



A 



Fig. 55. 



Fig. 56. 



74 MENSURATION. 

liter (1000 cu. cm.), one-half liter (500 cu. cm.), and 
one-fourth liter (250 cu. cm.), their capacity being marked 
upon them. For accurate measurements, fill the flask 
nearly to the mark, and placing the eye so that the mark 
appears as a straight line, drop in the liquid with a piece 
of glass tube * until the correct level is reached. If you fill 
above the mark, use the tube to withdraw some of the 
liquid. The flask should rest on a firm horizontal surface. 
It is well to mark the position of the line by a piece of 
paper, as described in the directions for using graduates. 

EXERCISE 3. 

PRACTICE IN DETERMINING VOLUMES. 

EXPERIMENT. 

Apparatus.— Method A: Graduated cylinder; body whose volume 
is to be measured; water. 

Method B: Piece of fine wire; cylinder; rubber band; paper for 
markers; body; water. 

Method C: Burette or equivalent; ungraduated jar or equivalent; 
rubber band; paper for markers; body; water. 

Object. — To determine the volume of an irregular body 
by displacement. 

Manipulation. — Method A. Fill the graduated cylin- 
der part full of water, read the volume (as a in Fig. 57), 
observing all the precautions given in the preliminary 
notes on determination of volume, and record the reading. 
Drop the body whose volume is to be determined (as e) into 
the cylinder, and again read the volume (as C). The dif- 
ference in the readings on the scale (a to C) is the volume 
of the body. 

Method B. Attach a fine thread or wire to the body 
whose volume is to be determined, and drop the body into 
the glass cylinder. Partially fill the cylinder with water. 

* As in using the shellac in the exercise on the lines of magnetic 
force. 



PRACTICE IN DETERMINING VOLUMES. 



75 




Mark the level of the water by means of a piece of paper 
about 4 cm. wide and long enough 
to be wrapped several times around 
the cylinder. Fasten this marker 
in position by a rubber band. Be 
sure that the upper edge of the 
paper is at the same level all 
around the cylinder, and that, when 
looked at horizontally, the line of 
the paper just touches the lowest 
point of the meniscus. By means 
of the thread remove the object, 
allowing as much of the water as 
possible to drain back into the 
cylinder. Run in water with a 
burette until the level in the cylin- 
der is the same as before. The 
volume of water run in, as measured 
on the burette, is the volume of the body. 

Method C. From a burette, run into a dry, empty 
cylinder any known volume of water, — say 50 cu. cm. 
— and mark its meniscus by a strip of paper as in B. 
Empty the cylinder, wipe it dry and put in the object 
whose volume is to be determined. Run in water from 
the burette until the level is the same as it was before; 
note the reading of the burette. The difference between 
the two volumes of water drawn from the burette is the 
volume of the object. For an object that floats, a sinker 
must be used. First get the volume of the sinker alone, 
attach the object to it, and get the volume of both ; then 
by subtracting the volume of the sinker from the volume of 
the two, the volume of the body alone can be obtained. 

Determine by each of these methods the volume of the 
same body. Compare the results, and state which is the 
best process in your opinion, and why. As many deter- 



76 



MENSURATION. 



minations should be made as time allows, and the results 
averaged. Arrange as follows : 



Method A. 


1st Trial. 2d Trial. 


Vol. water plus body = 


cu. cm. cu. cm. 


" " alone = 


" " " " 


" of body — 


" " " " 


Average vol. by A = 


cu. cm. 


Method B. 


1st Trial. 2d Trial. 


Burette-reading after running in, 


cu. cm. cu. cm. 


" before " " 


<( K «< tt 



Difference in burette-reading, 
or volume, 

Average vol. by B = 

Method C. 

Burette-reading after running in, 

i, << before " " 



cu. cm. 
1st Trial : Body out. 2d Trial. 



Volume run in, 

Burette-reading after running in, 
" " before " " 



Vol. run in, 

Vol. run into empty cyl., 
" " " cyl. + body, 



' ' of body, 
Av. vol. of body : 



cu. cm. 



EXERCISE 4. 

CROSS-SECTION AND INTERNAL DIAMETER OF A TUBE. 
EXPERIMENT. 

Apparatus.— Glass tube; burette or equivalent; markers; rubber 
band; cork; water; meter-stick. 

Object. — To find the cross-section and internal diameter 
of a tube by determining its length and volume. 



CROSS-SECTION AND DIAMETER OF A TUBE. 77 

Manipulation. — Method A. Cork one end of the tube, 
and pour in water enough to cover the cork to a depth of 
about 1 cm. Carefully mark the level of the 
water by means of a piece of paper and rubber 
band, as in the preceding experiment. Run in 
a known volume of water, say 40 or 50 cu. cm. 
Place on your tube a second measuring-paper, 
and move the paper until it just marks the level 
of the liquid when the tube is held vertically. 
The distance between the two water-levels, as 
indicated by the markers, is the height to which 
the known volume has filled the tube. Pour out 
the water and place the tube close against the 
meter-rod, taking care not to disturb the mark- 
ers. Record the distance corresponding to ab 
in Fig. 58. Then 

Volume 



Cross-section = 



Height ' 





— 1( 


^^^^ 









Fig. 58. 

Repeat several times with varying volumes. This will re- 
duce the errors due to the uneven bore of the tube. Ar- 
range the results as follows : 



No. Trial. 


Vol. run in. 


Height in Tube. 


Cross-section. 











Average cross-section = 
Method B. Place the two paper markers so that they 
are a certain distance apart * from upper edge to upper 
edge, as measured on the scale. Set the tube upright 
and run in water until the level of the liquid is just at the 
lower mark. Read the burette. Run in more water to 



* The distance between the markers should be an integral number 
on the scale. 



78 MENSURATION. 

the level of the upper mark, and read the burette again. 
The difference of the readings is the volume run in be- 
tween the markers. Repeat several times with the markers 
at various heights. Arrange results on the plan indicated 
in the preceding exercise. In Method A, the volume being 
measured to an integral number, the chief liability to error 
is in the determination of the height. In Method B, the 
lieiglit being measured to an integral number, the chief 
liability to error is in the determination of the volume. 
Therefore the values obtained by averaging the results of 
the two methods should be very nearly correct. 

To find the diameter, take the average value for the cross- 

D* 

section and substitute it for A in the formula, A = n— . 

4 

Determine the cross-section of a glass tube by both meth- 
ods, and, if so instructed, compute its diameter, calculating 
the internal diameter by this formula; carefully measure it 
according to notes on Measurement, and compare the cal- 
culated and the measured results. For comparison, take 
the average of the diameters of the two ends of the tube. 
All measurements of length should be made to 0.1 mm., 
and burette-readings to 0.1 en. cm. All values of cross- 
sections to be expressed in sq. cm., and carried out to fourth 
decimal place. Express the values of diameters in mm. to 
first decimal place. 

DETERMINATION OF WEIGHT. 

Introductory. — For exact comparisons of weights, units 
are required, as in comparisons of lengths or volumes. 
The ordinary English units are the pound (lb.), and the 
ounce (oz.), one sixteenth of a pound. The pound is a 
weight equal to that of a piece of metal in the posses- 
sion of the government. The metric unit of weight is 
the gram (g. or grm.), and is the weight of a cubic centi- 



DETERMINATION OF WEIGHT. 



79 



meter of water at a specified temperature. A larger unit, 
the kilogram (k.), is the weight of 1000 grams. The 
gram is divided into decigrams (d. or dg.), .1 gram ; centi- 
grams (eg.), .01 gram ; milligrams (mg.), .001 gram. Large 
weights are expressed in kilograms and decimals of a kilo- 
gram ; small weights in grams and decimals of a gram. 
In a general way, the kilogram, is used in place of the pound 
in English measure, and the gram in place of the ounce. 

The Balance. — This instrument is represented in Fig. 59. 
S is the support, BB the beam, and PP the pans. Before 
use the beam should be level, and the bottoms of the pans 
about half an inch from some surface underneath. The body 
to be weighed should be placed in the left-hand pan, and 




weights in the right-hand pan, one by one, until the beam 
again hangs level. Then the sum of the weights used is 
the weight of the body. The weights used in laboratories 
are generally metric. The larger ones down to one gram 
are made of brass (Fig. 60), and their values are stamped 
on the top. Weights of less than one gram are made of 
platinum or aluminium. These have values stamped on 
them in decimals of a gram.* For example, a weight 
marked 0.1 would be 0.1 (one tenth) of a gram, or a deci- 

* Sometimes the smaller weights are made of wire. The number 
of parts represented is indicated by bending the wire into a polygon 
of a corresponding number of sides. 



80 



MENSURATION. 



gram-; 0.02 means two centigrams, etc. The larger weights 
are kept in holes bored in a block of wood ; the smaller 
are either in one hole provided with a cover, or in shallow 
holes covered by a glass plate. In case the smaller weights 




are in one hole, they should be taken out and placed upon 
a piece of paper, marked as follows : 

.5 .2 .2 .1 

.05 .02 .02 .01 

Each w T eight should be laid so as to cover the mark cor- 
responding to it, and, except when in the scale-pan, should 
be kept there until the operation is completed. A glance 
at the uncovered numbers on the card then tells which 
weights are in the scale pan. Unless very heavy (say above 
500 grams), weights should be handled with the pincers 
provided for this purpose, and not with the fingers. All 
weights should be placed at once in the proper receptacle 
when removed from the scale-pan, and never allowed to lie 
on the table. The large brass weights are handled by the 
knob on top. Never allow the scales or weights to come in 
contact with anything that might corrode or injure them. 

Weights are of the following numbers and denominations: 
one five, two twos, and a one. Thus, the weights under one 
gram would be one-half gram (0.5 grm.), two one-fifth 
gram (0.2 grm.), and one one-tenth gram (0.1 grm.). Or 
there are one 100-grm., one 50-grm., two 20-grm., and one 
10-grm., etc. 

Time is saved by weighing in a methodical manner, and 
not taking weights at random. Usually the weight of a 
body can be estimated in round numbers, and the first 



DETERMINATION OF WEIGHT. 81 

weight tried should be about that estimated. For example, 
the body is estimated to weigh about 20 grm. Placing it 
in the left-hand pan, put a 20-grm. weight in the other. 
The weight-pan remains in the air, hence 20 grm. is not 
enough. Add 10 grm. more : this is too much. Replace by 
5 grm. : also too much. Replace by 2 grm. : now it is too 
little. Add 2 grm. : too little still. The weight must be 
between 24 and 25 grm. Add 0.5 grm. : too little. Add 0.2 
grm. more: too much. Replace by 0.1 grm. : still too little. 
Add 0.05 grm., and the correct weight is found. On add- 
ing up the weights in the scale-pan they amount to 

24.00 g 
6 dc. or .60 g. 
5 eg. or .05 g. 

24.65 g. 

Weights are usually expressed in grams and decimals of a 
gram. We would not say that a weight was 24 grams, 6 
decigrams, and 5 centigrams, but 24.65 grams; just as we 
do not say that a thing cost 2 dollars, 4 dimes, and 7 cents, 
but $2.47. 

In getting the weight of a liquid, one method is to first 
weigh the empty vessel, and then the liquid and vessel to- 
gether. For example, suppose 10 grams of a liquid are 
wanted. Weigh a vessel and then add 10 grm. to the 
weights on the pan and pour the liquid into the vessel until 
the beam balances. Arrange notes as follows, always plac- 
ing the weight of the dish alone on the lower line, since it 
is to be subtracted from the larger weight of the dish and 
liquid : 

Dish and liquid = 26.249 
Dish alone, = 16.249 



Liquid = 10.000 



82 



MENSURATION. 



/\ 



Another method, called counterpoising, is to place the 
vessel in one pan, and balance it by some substance, such 
as sand or shot, in the other. The weight of the liquid 
alone need not then be determined by actual weighing. It 
is generally easier to counterpoise a flask or dish than 
to weigh it accurately. 

The Spring-balance. — In this, the weight attached pulls 
out the spring and registers itself by a pointer on a scale 
engraved on the brass. The scale is generally graduated 
up to twenty-five pounds and reads down to one-half pound, 
/q\ every four pounds being numbered. In Fig. Gl 
P\ the long lines are pound marks, and the shorter 
lines between them, half-pound marks. In read- 
ing, be sure that the eye is directly over the 
pointer. Always read from the same side of the 
pointer, which is usually wide enough to cover 
half a pound on the scale. The scale is quite 
fine, and a magnifying-glass is often useful. As 
the pointer is liable to stick, it is well to shake 
the balance a little before reading. Be careful 
to hold it so that the rod to which the hook is 
attached can slide freely. This is especially 
needful when using the balance to measure force. 
Fig. 61. ij«] ie ]j a l ance must be held just in the line of the 
pull; otherwise it will bind and give incorrect readings. 
There are some balances which read to 48 pounds. In 
these the scale only reads to pounds. After being used to 
reading on a 24-pound balance, one is almost certain to 
make mistakes in reading on one of the 48-pound bal- 
ances. Balances reading up to 8 oz. are also used. The 
scale reads to i oz. In using one of these balances, 
fractions of less than one scale-division should be estimated 
by the eye. With practice one should be able to read to 
■£$ of an ounce (.037 oz.). Never leave a balance stretched 
out any longer than necessary, as it injures the spring. If 



PRACTICE IN WEIGHING. 



83 



the pointer does not stand at when there is no pull on 
the spring, read the position of the index before beginning 
to weigh, and subtract (if over 0) from subsequent read- 
ings. Thus, if the pointer read one-half pound, all read- 
ings are half a pound too high, and half a pound must be 
subtracted.* A spring-balance is generally used to measure 
forces; it is then often called a Dynamometer, i.e., "force- 
measurer." When a spring-balance is used for weighing, 
it should never be held in the hand, but suspended from 
some solid object. 

EXERCISE 5. 

PRACTICE IN WEIGHING. 
EXPERIMENT. 

Apparatus.— Scales; weights; avoirdupois weights or 8-oz. bal- 
ances (if the latter, one to three students is enough). Several bodies 
weighing one to two ounces. 

Object. — To determine the value of the ounce in grams. 

Manipulation. — Weigh some body to 0.01 grm. on the 
scales.f Determine the weight of the same body in ounces 
by means of a spring-balance or by the scales and English 
weights. From the following proportion calculate the 
number of grams to the ounce: 

wt. in oz. : wt. 1 oz. ::wt. in grms. : x. 
x = no. of grms. to the oz. 

Kepeat with as many different substances as time allows, 
average the values so obtained, and tabulate the results as 
follows : 



Body. 


Wt. in oz. 


Wt. in grm. 


Grm. per oz. 











* This is often called the zero error. 

f Select some body weighing 30 to 60 grm. In a general way, the 
heavier the body, the more accurate the results. 



84 



MENSURATION. 



EXERCISE 6. 

EXPERIMENT. 

Apparatus.— Part I. Meter-stick; blocks of wood; lead-pencils; 
books; etc. 
Part I. Tumbler; measuring-cylinder; water. 
Part III. Scales and weights; bodies weighing from 10 g. to 50 g. 

Object. — To practise estimating values in the Metric 
system. 

Manipulation. — Length. Estimate carefully, by the eye 
alone, the dimensions of one of the blocks, the meter-stick 
being out of sight. Record the estimate. Carefully meas- 
ure the same distance and record. Try this a number of 
times, varying the distances measured each time until esti- 
mates on several different lengths in succession come quite 
near to measured values. Record as follows : 



Estimated. 


Found. 


Difference. 









The figures in the third column are got by finding the 
difference between the measured and the estimated dis- 
tances. If the estimate is less than the true distance, the 
difference has the minus sign; if greater, the plus sign. It 
is best to select lengths ending in sharp corners, distances 
between points marked by a pencil, etc. 

Volume. Put some water into the tumbler, estimate the 
volume in cu. cm. Measure the volume, repeat with vari- 
ous volumes, and record as above. If possible, change the 
vessel used to hold the water. 

Weight. Estimate the weight of a few bodies in grams. 
Weigh the bodies. 



NOTES ON ERRORS. 85 

Measure as accurately as possible, but do not try to esti- 
mate too closely. It is enough to get within 0.5 cm. of 
correctness in length, one centimeter in volume, and one 
gram in weight. 

NOTES ON ERRORS. 

The results of measurements are never absolutely correct. 
This is because of imperfections in the apparatus and mis- 
takes of the experimenter. In physical experiments, any- 
thing due to these causes, which tends to make results 
incorrect, is called an error. Errors of the experimenter 
are called Personal Errors. For example, in Experiment 
1, any mistake in estimating the fraction of a mm., in 
not reading the scale correctly, or not placing it properly 
on the table, would be a personal error. Personal errors 
may be often avoided by using care, and their effect on the 
result may be still further reduced by averaging. In esti- 
mating the fraction of a millimeter, a person is just as 
liable to over-estimate as to under-estimate ; if he makes a 
number of determinations, and averages his results, the 
over-estimates and the under-estimates will tend to neutral- 
ize each other, and the average will be nearer the truth. 
For this reason, in conducting an experiment calling for 
measurement, the more carefully the work, and the greater 
the number of determinations, the closer to the truth will 
be the average result. Errors due to the apparatus are 
called apparatus errors. An error which produces a con- 
stant effect, always tending to make the result too high 
or too low, is called a constant error. For example, in 
Method B, Ex. 3 (Volume of an Irregular Body), when 
the body was removed from the water it took some water 
with it. The volume obtained included this water, and 
was always higher than the truth. Sometimes the value 
of a constant error can be determined and eliminated. 
Suppose a spring-balance with no weight attached reads 



86 MENSURATION. 

1 lb., then every reading on the balance will be 1 lb. high, 
and the true weights can be obtained by subtracting 1 lb. 
from each weight as given by the balance. 

Questions. — 1. Why were a number of determinations 
made in Ex. 1, and the results averaged ? 2. What were 
some of the personal errors in Ex. 1 ? What was an appa- 
ratus error in Ex. 2? Were there any constant errors in 
this Exercise ? Prepare a list of the personal and appara- 
tus errors in each experiment in this chapter, with sug- 
gestions for their avoidance. 

EXERCISE 7. 

PHYSICAL AND CHEMICAL CHANGE. 

Preliminary. — Are physical and chemical changes accom- 
panied by change in weight? As good examples of physi- 
cal change we may take, first, the solidifying of a liquid 
(that is, the changing of it from a liquid to a solid when 
cooled), and, second, the dissolving of a solid, in both cases 
observing the weight before and after the change. In 
selecting an example of chemical change, we must take 
two substances whose union will give a new substance, mix 
known weights of each, and weigh the products. We can 
then compare the weight of the new substance formed, 
with the sum of the weights of the original substance. 

EXPERIMENT 1. 

Apparatus.— Scales and weights; test-tube and fine wire to sus- 
pend it; shavings of wax or paraffiue; means of heating; bits of 
solid caustic potasb; water; solutions " No. 1 " and " No. 2 " ; two 
small vessels in which liquids may be weighed. 

Object. — To see if the weight of substances is the same 
before and after a physical change. 

Manipulation. — (a) Place some scraps of wax or paraf- 
fine in a test-tube. Suspend the tube from one end of a 
balance and gently warm it until the solid melts. Counter- 



NOTES ON ERRORS. 87 

poise and watch while the contents of the tube cool again. 
What sort of a change have you here ? How do the weights 
of the solid and liquid compare ? (b) Suspend a test-tube 
half full of water from one arm of your balance, by means 
of a thread, and place a small piece of caustic potash on a 
scrap of paper in the pan. Counterpoise. Drop the solid 
into the water, leaving the paper on the pan. "Watch for 
any change in weight while the solid dissolves in the liquid. 
What sort of a change is this ? What is your inference ? 
If these experiments illustrate a general law as regards 
change of weight during a physical change, what do you 
infer the law to be ? 

EXPERIMENT 2. 

Object. — To see if the weight of substance is the same 
before and after a chemical change. 

Manipulation. — Put a small glass vessel on the left- 
hand scale-pan and record the weight. Add a 10-gram 
weight to the right-hand scale-pan. Pour some of solu- 
tion No. 1 slowly into the vessel until it nearly balances 
(in all probability you cannot get it to exactly balance) ; 
change the weight on the scale-pan until you have the 
exact weight of the vessel -f- the liquid. Record and find 
the weight of the solution alone. Weigh in the same man- 
ner a part of solution No. 2. The quantity must be 
exactly determined, but need not be exactly equal to that 
used of No. 1. Pour the contents of one vessel into the 
other ; note what occurs, and weigh the whole. From this 
weight subtract the weight of the vessel, and you have the 
weight of the contents. Compare this weight with the 
sums of the weights of the two liquids. Have we changed 
our forms of matter ? Is this change chemical or physi- 
cal ? During a chemical change, what is true as regards 
the weight of matter? This experiment illustrates a gen- 



88 



MENSURATION. 



eral law. From your work, can you state the law ? Ar- 
range the results as follows : 



Weight of solution No. 1 -}- vessel 
" vessel 

" solution alone 

" solution No. 2 -f- vessel 
" vessel 



= grm. 



" solution alone = 

" two solutions -f vessel = 

" vessel = 

" two solutions alone = 

" No. 1 = 

" No. 2 • = 

" both solutions weighed separately = 



DENSITY AND SPECIFIC GEAYITY. 
EXERCISE 1. 

DEXSITY AND ITS DETERMINATION. 

Preliminary. — The same weight of matter may take up 
a great deal of room or only a little. We express this 
quality of bodies by the words "heavy" and "light." 
When we say that a body is " light/' we mean that the 
space it occupies, its volume, is great compared with its 
weight, and by the use of the word "heavy" we mean the 
reverse. In using these words we always refer to some 
other bodies. Thus, when we say that gas is light, we 
mean that the relation of its volume to its weight is 
smaller than that of most bodies. Suppose, now, we com- 
pare a stone and a piece of lead. By very rough tests we 
can determine which is the heavier ; but if any exact com- 
parison is desired, the relation of volume and weight must 
be expressed as a number. To get this number, we must 
measure the volume and weight of each body, and divide 
the weight by the volume. The quotient shows how many 
times the volume number is contained in the weight num- 
ber. A number which, like this, expresses the number of 
times one quantity is contained in another is called a ratio. 
The ratio of the weight of a body to its volume is called 
the density of the body. By comparing the density num- 
ber for lead with the density number for stone, we can 
determine just how many times the lead is denser than the 
stone. Density is sometimes represented by the sign A ; * 

* Called delta. 

89 



90 DENSITY AND SPECIFIC GRAVITY. 

w 
and so we can write* A = — , or density is the weight of 

the unit of volume. Would these numbers be the same 
for different systems of measurement ? 

EXPERIMENT. 

Apparatus.— Scales and weights ; 8-oz. balance or English 
weights ; measuring-cylinder ; bodies whose densities are to be 
determined ; measuring-sticks (English and French). 

Object. — To determine (1) the density of the given 
substances (a) in the Metric system, (b) in the English 
system, ounces to the cubic inch and pounds to the cubic 
foot ; and (2) the order in which the substances should be 
arranged as regards density. 

Manipulation. — (a) Determine the weight of each 
body in grams, weighing to 0.1 grm. and its volume in 
cu. cm. If the body is a geometrical figure, measure the 
dimensions of the figure and calculate the volume. If the 
body is irregular, get its volume by one of the methods 
given in the exercises on mensuration. Find the density 
by dividing the weight by the volume. Carry this number 
out to the second decimal place. 

(b) Determine the weight of each body in ounces by a 
spring-balance, f expressing fractions of an ounce as deci- 
mals. If possible measure the volume in cu. in. ; if it is 
not possible, calculate the volume in cu. in. from the vol- 
ume in cu. cm., as already found. 1 cu. cm. = 0.061 cu. 
in.; hence, Vol. in cu. cm. X 0.061 = vol. in cu. in. Cal- 
culate the density in English measure, (1) ounces per cu. 
in., (2) pounds per cu. foot. Arrange the results in two 
tables, heading the first table, " Table I, French," and the 
second, " Table II, English, as follows:" 

* Such an algebraic arrangement of symbols, as a short way of 
giving a rule, is called a formula. 
f An 8-oz. balance is the best. 



DENSITY AND ITS DETERMINATION. 91 

Table I, French. 



Body. 


Weight. 


Volume. 


Density. 











(2) Arrange the bodies in the order of their densities, 
that having the greatest density heading the list. 

Weigh the liquid in a small vessel in the usual way. In 
case the vessel is too large for the scale-pan, make a bale 
of string or wire, like the handle of a pail, and suspend 
the vessel below the scale-pan, as in Fig. 62. Be careful 
that the string or wire by which it is suspended does not 
break, and allow it to drop. 

Unit of Density.— We need some standard with which 
to compare densities. Some density must be taken as the 
unit, and all densities expressed in terms of that unit. 
The density of water at a specified temperature is used as 
the unit for solids and liquids, and that of air under fixed 
conditions of temperture and pressure, for gases. In com- 
paring the densities of solids or liquids, we take the num- 
bers obtained by dividing each density by that of water. 

Specific Gravity. — The number which shows how many 
times the density of water is contained in the density of 
any solid or liquid is called the Specific Gravity of that 
body. Thus, if the density of iron were 437.5 lbs. per ft., 
its specific gravity would be found by dividing its density, 
437.5 lbs. by 62.5 lbs., which is the density of water ex- 
pressed in the same system. We find that the density of 
iron is seven times that of water, hence the specific gravity 
of iron is 7. Calculate the specific gravities of the bodies 
whose densities you determined in Exercise 1. Are the 
specific-gravity numbers the same for all the systems of 
measurement used ? 



92 DENSITY AND SPECIFIC GRA VITY. 



EXERCISE 2. 

DETERMINATION OF SPECIFIC GRAVITY. 

Preliminary. — In order to determine the specific gravity 
of a body we conld get its density, as in Ex. 1, by dividing 
its weight by its volume. The density so obtained would 
be divided by the density of water (if not known, this 
would have to be found) ; the quotient would be the spe- 
cific gravity of the body. Or, again, to simplify the pro- 
cess, we could take equal volumes of water and the body 
under examination. Thus, if any volume of a body weighs 
50 grm., and an equal volume of water weighs 10 grm., 
then the density of the body is five times that of the water, 
and the specific gravity is five. 

Suppose we take a bottle, weigh it, then fill it completely 
full of water and weigh it again. The weight of the 
bottle subtracted from the combined weight of the bottle 
and water gives the weight of the water. Suppose, now, 
we empty the water completely out, and fill the bottle with 
the liquid whose specific gravity we wish to determine. 
Then, since we have the same bottle, and have filled it 
completely full, we have the same volume of liquid that 
we took of water. If we weigh the bottle and liquid 
together, and subtract the weight of the bottle, we get the 
weight of the liquid. Having the weights of equal bulks 
of water and the liquid, we can get the specific gravity 
of the liquid by dividing the weight of the liquid by the 
weight of the water. 

EXPERIMENT. 

Apparatus.— Scales ; weights; specific-gravity bottle ; liquid whose 
specific gravity is to be determined ; water. 

Object. — To determine the specific gravity of a liquid 
by the method of the " Specific-gravity Bottle." 



DETERMINATION OF SPECIFIC GRAVITY. 



93 



Manipulation. — Weigh the bottle with the stopper in. 
Be sure that it is perfectly dry. Fill it 
to the top with the liquid, and, holding it 
over some vessel to catch the overflow, 
slowly insert the stopper squarely, as in 
Fig. 61. During this operation the liquid 
should run over the rim of the bottle all 
around. With care, the bottle will be 
completely filled. To test this, turn the 
bottle upside down and see if any air 
bubbles appear. If they do, the bottle is 
not entirely full, and the operation of fill- 
ing must be repeated. Wipe the outside 
of the bottle dry and weigh it. Pour the liquid back into 
the "stock-bottle," rinse the gravity-bottle, fill it com- 
pletely with water with the same precautions as before, and 
weigh it. Arrange results as follows : 




Wt. bottle + liquid = 
" " alone = 



liquid 



Wt. bottle -\- water = 
" " alone = 



Wt. of liquid 



Questions. — 1. What is the principle of this experi- 
ment? 2. Why must you be sure that the bottle is com- 
pletely full each time ? 3. What do you consider the most 
important error that is likely to be made? 4. Why must 
the same bottle be used each time ? 5. Why should the 
bottle be rinsed out before filling it with water ? 



EXERCISE 3. 

THE WEIGHT LOST BY A BODY WHEN IMMERSED IN A LIQUID. 

Preliminary. — We know that a body does not weigh as 
much under water as it does above, and that when it is 



94 DENSITY AND SPECIFIC GRAVITY. 

completely immersed it displaces a volume of water equal 
to its own volume.* The object of the following exercise is 
to see if there is any connection between this loss of weight 
and the weight of the water displaced. On what principle 
must we work in order to be able to make this compari- 
son? 

In order to get the loss of weight, we can weigh the body 
in air and then in water. The difference is the body's 
loss of weight. To weigh the water displaced, we can fill 
the specific-gravity bottle completely full of water, and 
weigh it and the body together. Then if we put the body 
into the bottle it will crowd out a volume of water equal 
to its own volume. If, after inserting the stopper, we 
weigh the bottle with the remaining water and the body, 
the weight will be less than before by the weight of the 
water crowded out. This difference is the weight of the 
displaced water. Having found the body's loss of weight 
and the weight of the displaced water, we can see if there 
is any connection between the two facts. 

EXPERIMENT. 

Apparatus.— Specific-gravity bottle; water; scales and weights; 
solid body; fine wire for suspension; tumbler. 

Object. — To compare the weight lost by a body when 
immersed in a liquid, with the weight of a volume of the 
liquid equal to the volume of the body. 

Manipulation. — Fill the specific-gravity bottle full of 
water and place it in the scale-pan. Place the body in the 
same pan and weigh both. Take the stopper out of the 
bottle, put in the body, replace the stopper, wipe the bottle 
dry and weigh again. The difference in the weights is the 
weight of the water crowded out of the bottle when the 
body was put in, and hence the weight of a volume of 
water equal to the volume of the body. 

* Provided, of course, the liquid does affect on the solid. 



BODY IMMERSED IN A LIQUID— WEIGHT LOST- 95 

To get the body's loss of weight in a liquid, suspend it 
by a thread, or, better, a fine wire, which, as shown in Fig. 
62, passes through holes in the scale-pan .and box, and is 
attached to the scale arm-hook. Weigh. Put a tumbler 
of water under the box and adjust it so that the body is 




completely immersed in the liquid and touches neither the 
sides nor the bottom. "Weigh the body, being careful to 
keep it entirely under water. If time allows, repeat with 
some other liquid. Eecord results as follows : 

Bottle + water + body outside = 

« _|_ « _|_ « inside = 
Weight of water displaced = 

Weight of body in air = 

" " " " water = 



Loss of weight 



96 DENSITY AND SPECIFIC GRAVITY. 

EXERCISE 4. 

THE DETERMINATION OF SPECIFIC GRAVITY BY IMMERSION. 

Preliminary. — It is evident that the method of the spe- 
cific-gravity bottle cannot be used for solids, and so the 
principle of the preceding exercise is employed in deter- 
mining the weight of the water equal in bulk to the solid 
whose specific gravity is required. By weighing the solid 
in air and then in water we can get its loss of weight, which 
last, we have found, is also the weight of an equal volume 
of water. We then have the weight of the body and the 
weight of an equal volume of water, and can calculate the 
specific gravity. 

The same principle can be used in getting the specific 
gravity of liquids. By ascertaining the loss of weight of 
a solid in water, we get the weight of a volume of water 
equal to the volume of the solid. By finding the loss of 
weight of the same solid in the liquid whose specific gravity 
is to be determined, we get the weight of a volume of the 
liquid equal to the volume of the solid. The body being 
the same, we have the weights of equal volumes of the 
liquids, and can compute the required specific gravity. 

EXPERIMENT 1. 

Apparatus.— Scales and weights; body and wire for suspension; 
tumbler; liquid whose specific gravity is to be determined; water. 

Object. — To determine the specific gravity of a solid 
not affected by water, and of a liquid, by the method of 
" Double Weighing." 

Manipulation.— Part I. Suspend the solid by a thread 
or fine wire, as in the preceding exercise (Fig. 62). Care 
must be taken not to let the solid touch the glass at any 
point.* Weigh the solid as closely as can be done on the 

* With an irregular body, a glass stopper for instance, some judg- 
ment must be exercised regarding the manner in which the body is 
suspended. 



SPECIFIC GRAVITY DETERMINED BY IMMERSION. 07 

scales. Record the weight. Fill the tumbler with water 
and weigh again, taking care that the body is entirely im- 
mersed and touches neither the sides nor the bottom of 
the glass, and that the suspending thread does not touch 
the sides of the hole in the box. Record as follows : 

Wt. in air = 
" " water = 

Loss of " " " = 

Sp. gr. = ^ i ' . T— = rCarry out to 2d dec. pl.l 

r ° Loss of wt. m water L J r J 

Part II. After weighing the body first in air and then 
in water, and recording the weights, empty the water out 
from the tumbler, fill the tumbler with the given liquid, 
and weigh the body again, using in all cases the same pre- 
cautions as in Part I. Record results as follows : 

Wt. 



Loss of 



How does this experiment compare in principle with the 
method of the specific-gravity bottle ? 

If Part II is performed immediately after Part I., the 
solid's loss of weight in water is already known, and we 
have only to weigh the solid in the liquid whose specific 
gravity is required. The record would then take the fol- 
lowing form : 

[From Part L] Wt. in air = 

" " liquid = 

Loss of " " " = 
[From Part L] « " " " water = 



in air 


= 




Wt. 


in 


air 


— 


" water 






a 


a 


liquid 


= 


a a 


= 


Loss of 


a 


a 


a 




grav. = 


Loss wt. 
Loss wt. 


in liquid 
in water 


= 









98 DENSITY AND SPECIFIC GRAVITY. 

„ _ Loss of wt. in liquid _ 

V' ° ~ Loss of wt. in water ~" 

EXPERIMENT 2. 

Apparatus.— Scales and weights; water; tumbler; body lighter 
than water; sinker; thread or fine wire. 

Object. — To determine the specific gravity of a body 
that will float in water. 

Manipulation". — Weigh the body in air. Attach the 
sinker close to the body with thread or wire; suspend the 
two, as in the previous experiment, and with the same 
precautions determine the weight of the two in air. De- 
termine the weight of the two when immersed in water, in 
the same way as in the previous experiment. Remove the 
body and determine the weight of the sinker alone when 
immersed in water.* Arrange results as follows: 
Sinker + body in air — 
fS alone in air = 
Body in air = 

Sinker in water = 

Calculation. — Arrange calculations as follows: 
Sinker -f- body in air = Sinker in air = 

" " " water = " " water = 

Loss of wt. of both in water = Loss of wt. of sinker = 
Loss of wt. of body -J- sinker = 
" " " " sinker alone = 



Sp. grav. 



< " body " = 

Wt. of body in air 
Loss of wt. of body in water 



* The number of operations involved in this experiment may be 
reduced by taking the data obtained in Experiment 1, which may 
be done by using for a sinker the body whose specific gravity was 
there determined. It is then only necessary to ascertain the weight 
of the sinker plus the body in air and the loss of weight of both in 
water. 



LIQUID PRESSURE DUE TO WEIGHT. 



99 



Questions. — 1. In these experiments, is the weight of the 
equal volume of water actually measured at all ? 2. Why 
are you justified in taking the loss of weight as the weight 
of a bulk of water whose volume equals that of the body? 
3. State the principles of this experiment. 4. How does 
it differ from that used in getting the specific gravity of a 
liquid ? 

EXERCISE 5. 

LIQUID PRESSURE DUE TO WEIGHT. 

Preliminary. — For investigating the conditions affectiag 
liquid pressure, we use the apparatus shown in Fig. 63. A 
pressure-gauge is made of a glass funnel, a, whose end is 




} 



covered with thin rubber, h. From the other end, a rubber 
tube, ?, connects the funnel with the glass tube, cd, which 



100 DENSITY AND SPECIFIC GRAVITY. 

is attached to the scale, m, and contains a drop of water, 
d, to act as an index. Changes of pressure will cause the 
rubber, k, to bulge more or less, and this will cause a 
motion of the index which can be read upon the scale. 
This gauge is hung from the block, e, by a wire on which 
it turns, so that it may be made to face in any direction 
and the centre of k remain at the same depth. To this 
block is attached a meter-stick, f, which indicates the 
depth. The apparatus is held by a clamp, g, and is placed 
in a pail of water, li. The scale m lies flat upon the table. 

EXPERIMENT. 

Apparatus.— As shown in Fig. 63. Water and pail (or equivalent); 
measuring-cylinder (or something that can be used to produce 
changes in depth directly over the gauge-face.) 

Object. — To investigate the conditions affecting the 
pressure of a liquid upon a surface immersed in it. 

Manipulation. — Before comm encing the experiment 
it is necessary to know how the movements of the index 
correspond with changes in pressure. The gauge being in 
the water, press on its face gently with the finger and note 
the direction of the movement of the index. Remove the 
pressure and note again. Record the direction of move- 
ment for increased and decreased pressure, as follows : 
Increased pressure-index moves 
Decreased " " " 

Part I. Effect of depth. The gauge-face being 1 or 2 
cm. below the level of the liquid, note the position of one 
end of the index, and the depth of the gauge. Increase 
the depth 4 or 5 cm. (most easily done by setting the 
clamp lower down on the rod), read the depth and the 
position of the index. Be careful to always read from 
the same end of the index, to clamp the apparatus firmly 
at each depth, and to wait for the liquid to come to rest 
before reading. In this way take readings at various 
depths, working first down to as near the bottom of the 



LIQUID PRESSURE DUE TO WEIGHT. 



101 



vessel as is possible, and then up again to near the surface. 
Tabulate results as follows : 



Depth. 


Index-reading. 


- 





From the study of these figuures, place in the note-book 
an inference regarding the effect of depth on pressure. 

Part II. Effect of direction. Adjust the apparatus so 
that the gauge-face is 6 or 7 cm. below the surface. Put- 
ting the hand into the water, take the rubber tube gently 
between the thumb and finger at a point just below where 
it joins the glass, and slowly turn the gange-face in various 
directions, reading the index for each direction. Take 
care that there is plenty of slack rubber tube, and that it 
does not " kink" anywhere. Make three or four trials at 
this depth, and then repeat at some other. Eecord results 
as follows: 



Depth. 


Direction of gauge-face. 


Index-reading. 









What inference ? 

Part III. Effect of distance from sides of vessel at same 
depth. Gently set the gauge at various points at the same 
level by moving either the arm of the clamp horizontally 
or the pail under the apparatus. In each case wait for the 
liquid to come to rest, read, and record as follows : 



Depth. 


Position relative to vessel sides. 


Index-reading. 









What inference ? 



102 



DENSITY AND SPECIFIC GRAVITY. 



Part IV. Effect of depth of liquid directly over the 
immersed body. Tip the apparatus sideways as shown in 
Fig. 64, and clamp it there. Bring the bottom of a glass 




cylinder down over the gauge-face, as in the figure. This 
reduces very much the depth and amount of the liquid 
directly over the gauge-face, but does not change the gen- 
eral level of the liquid to a noticeable degree.* Immerse 
the bottom of the cylinder to various distances above the 
gauge-face. Read the index each time. At each point 
hold the cylinder steady and wait until the water in the 
pail has come to rest before reading the index. To in- 
crease the depth of liquid directly over the gauge-face, 
submerge the cylinder completely and invert it. Holding 
the inverted cylinder by the bottom, raise it until the lower 
end is only one or two cm. below the level of the liquid. 
So long as no air enters, the water will remain in the cylin- 
der, and by bringing it over the gauge-face, as in Part IV, 
the depth of water there may be made considerably greater 



■ Of course, the larger the pail, the less this error amounts to. 



SPECIFIC GRA VITT OF LIQ UIDS B Y BALANCING. 1 03 

than elsewhere in the pail. The admission of air into the 
cylinder, by raising one edge for an instant above the level 
of the liquid, will enable yon to change the depth of water 
in it. In this way try various depths. Record resnlts as 
follows : 



Depth of Gauge-face below 
General Surface. 


Depth Liquid directly 
above Gauge-face. 


Index- 
reading. 









What inference ? 

Write out a summary of what you have learned about all 
the conditions affecting the pressure that the weight of a 
liquid causes it to exert on an immersed surface. 



EXERCISE 6. 

SPECIFIC GRAVITY OF LIQUIDS BY THE METHOD OF BALANCING. 

Preliminary. — In the following exercise we wish to de- 
termine the specific gravity of a liquid by the method of 
balancing. This method is based 
on the laws of liquid pressure. 
Suppose we have two tubes, con- 
nected as at a in Fig. 65. Pour 
some liquid into one tube, and a 
liquid that will not mix with it 
into the other. Then, when the 
liquids have come to rest, we shall 
have two columns balancing each 
other. Where the two liquids join, 
a, there are two pressures — a down- 
ward pressure due to the weight of 
the liquid above, and an upward * IG " ° ' 

pressure due to the liquid in the other tube. When the 




104 



DENSITY AND SPECIFIC GRA VITY. 



liquids have come to rest, we know that these pressures are 
equal. Call the upward pressure P, and the downward 
pressure P' ; then P = P\ But we know that 



and 



P = aX D X A, 
P> = a ' X D' X A', 

calling a', D', and A' the values for the second liquid. So 

aXDx A = a' xD' X A\ 

But as the pressures come together in the same tube at the 
same point, a = a', so when two liquids come to rest in 
communicating vessels, 

DxA = D' X A', 

or, the depth times the density of one equals the depth 
times the density of the other. Hence, to determine the 
required density, we have only to put into one tube a liquid 
of known density, into the other the liquid under examina- 
tion, measure the depths of the two liquids, and divide the 
product of the density and depth of the former by the 

depth of the latter, or A' = —, — 

EXPERIMENT. 

Apparatus.— As shown in Fig. 66. Funnel; water and oil— with 
vessels to contain them; meter-stick; solution of copper sulphate 
or equivalent. 

Object. — To determine the specific gravity of a liquid 
bv the method of balancing.* 



* Observe that this special method can only be used for liquids 
that do not mix. 



SPECIFIC GRA VITY OF LIQ UIDS BY BALANCING. 105 



Manipulation. — By the aid of the funnel, pour water 
into the tube until it stands about half-way up in both 
branches. Make sure that 
no air remains in the rub- 
ber tube by drawing the 
tube through the fingers 
pressed together. Slowly 
pour the oil into the larger 
tube, at first letting it run 
down the sides so as to ac- 
cumulate quietly on top of 
the water, and continu- 
ing until the column is 
50 cm. or so long. Care 
must be taken that the 
junction of the liquids does 
not get below the glass into 
the rubber tube. In case 
this happens, it can some- 
times be remedied by pour- 
ing more water into the 
water tube. Avoid getting = 
the oil into the water tube. 

When the liquids have come to rest, starting from some 
horizontal line below the tubes, as D, Fig. 63 (the floor, 
the base-board, or the table will do), measure the distance: 

(a) from the reference-line to the top of the water col- 
umn, or DA; 

(b) from the reference-line to the top of the other col- 
umn, DB; 

(c) from the reference-line to the junction of the liquids, 
marked DC. 

Calculation. BD — CD = Height of the column of 
the liquid whose specific gravity is to be determined, and 




106 



DENSITY AND SPECIFIC GRA VITT. 



AD — CD = Height of the water column producing the 
same pressure on the same area. Therefore 

A-G 



Sp. grav. = 



B- C 



Make three or four determinations with various heights, 
changing the heights by pouring in either water or oil. 
Tabulate results as follows: 









TABLE I. 




BD 


AD 


CD 


BD - CD 


AD -CD 


Sp. Grav. 















If time allows, repeat, using solution of copper sulphate 
as the liquid whose specific gravity is to be determined, 
and the oil as the liquid of known density, taking for its 
specific gravity the average of three trials with water. 



EXERCISE 7. 

EXPERIMENT 1. 

Apparatus.— Loaded test-tube with cork and weights; measuring- 
cylinder; water; other liquids of known density. 

Object. — To compare the weight of a body that will 
float with the weight of the liquid displaced by the body 
when floating. 

Manipulation. — Weigh the test-tube; pour about 30 
cu. cm. of some liquid into the measuring-cylinder, care- 
fully read the volume, and holding the test-tube by the 
cork, let it slip gently into the liquid until it floats. Be 
careful that the measuring-cylinder is dry above the level 
of the liquid after the test-tube is inserted. In order that 
the body may float freely, tap the measuring-cylinder sev- 
eral times with a lead-pencil. Again read the volume of 



ATMOSPHERIC PRESSURE AND THE BAROMETER. 107 

the liquid. The difference in the readings gives the vol- 
ume of liquid displaced by the body, and this volume 
multiplied by its density gives the weight. Repeat the 
determination with two other liquids. Record results as 
follows: 



Vol. before. 


Vol. after. 


Vol. displaced. 


Weight i Liq. 
displaced. , used. 


Wt. of 
Body. 















EXPERIMENT 2. 

Object. — To determine the specific gravity of a liquid 
by the use of a floating body. 

Manipulation. — With the apparatus above, determine 
the specific gravity of another liquid, writing out in the 
note-book a complete statement of the special method, etc. 

Questions. — 1. State the principle of these experiments. 
2. How does it differ from that on which the preceding 
exercises were based? 3. How does the loss of weight of 
the body compare with its weight in air ? 4. Do you think 
this fact had any connection with the floating of the body ? 



EXERCISE 8. 

ATMOSPHERIC PRESSURE AND THE BAROMETER. 
EXPERIMENT. 

Apparatus.— Barometer tube; clamp; handkerchief or cloth; mer- 
cury (about 1 k.) funnel ; feather on wire for removing air-bubbles ; 
dish to hold mercury; meter-stick; scales and weights; beaker glass 
for weighing mercury. 

Object. — To measure the pressure of the atmosphere. 

Manipulation. — Clamp the barometer-tube in an up- 
right position, closed end down, placing under it some soft 
substance, as a handkerchief or towel. By the aid of the 
funnel fill the tube about half full of mercury, then gently 



108 DENSITY AND SPECIFIC GRAVITY. 

insert the feather, and, by turning the wire, remove the 
bubbles of air which adhere to the side. Add. 10 or 15 cm. 
more of mercury and repeat the removal of the air-bubbles. 
Proceed in this way until the tube is filled with mercury 
and contains no air. Have ready the dish containing the 
mercury filled to a depth of 3 or 4 cm.; grasp the tube 
near the top with the right hand, placing the thumb firmly 
over the opening. With the left hand unclamp the tube, 
grasp it near the bottom, and (keeping the thumb firmly 
on the open end) inverting the tube, place the end in the 
vessel below the level of the mercury. Kemove the thumb 
and again clamp the tube vertically, being sure that the 
clamp takes the weight of the tube, which must not rest 
on the bottom of the vessel. Observe and record what 
happens. 

When the mercury column has come to rest, carefully 
measure its height above the level of the mercury in the 
vessel. Placing the thumb loosely over the lower end of 
the tube and holding the tube as before, raise it gently 
until its lower edge is just below the level of the mercury, 
then press the thumb firmly on the bottom, lift the tube 
out, incline it in a nearly horizontal position, and allow the 
mercury to run very gently into the thin glass vessel by 
admitting air, a few bubbles at a time, into the bottom of 
the tube. Be sure that none of the mercury is spilled. 
Weigh the vessel with the mercury, and also weigh the 
empty vessel and compute the weight of the mercury. This 
gives the pressure of the atmosphere on each area equal to 
that of the cross-section of the tube. 

Calculation". — To find the cross-section of the tube, 
divide the weight of the mercury by 13.6 to get the vol- 
ume, and this quotient in turn by the height, as in the ex- 
periment on the Cross-section of a Tube. To find the 
pressure per sq. cm., make the proportion A : 1 sq. cm. :: 



SPECIFIC GRAVITY OF TWO LIQUIDS. 109 

W : W. Where A is the area of the tube, W is the weight 
of the mercury, and W is the weight per sq. cm. 



EXERCISE 9. 

SPECIFIC GRAVITY OF TWO LIQUIDS BY BALANCING AGAINST 
THE ATMOSPHERIC PRESSURE. 

Preliminary. — If we dip the lower end of a tube into a 
liquid and remove a portion of the air from the tube, the 
tension of the air remaining becomes less than that of the 
air outside, and a column of the liquid is forced up the 
tube, until its weight, plus the tension of the air above it, 
produces a pressure equal to the tension of the air outside. 
If we place the tube in another liquid and withdraw the 
same amount of air, then the second liquid-column formed 
has to furnish the same pressure as the first. The two 
columns, instead of being balanced against each other, as 
in Exercise 6, are balanced against the same pressure, that 
of the atmosphere, and must be of equal weight. So, as 
before, 

A X D = A' X D\ 

In the following exercise we wish to determine the spe- 
cific gravity of a liquid by this method. In order to have 
the same reduction of tension in each tube, both are con- 
nected with the same vessel, as in Fig. 67, and the air drawn 
out of that. If one liquid has a known density, we can 
determine the specific gravity of the other, by the same cal- 
culation as in Exercise 6. 

EXPERIMENT. 

Apparatus.— Form shown in Fig. 67. Vaseline; meter-stick; water; 
solution of copper sulphate and some other solution. 

Object. — To determine the specific gravity of a liquid 
that will mix with water, by the method of balancing. 



110 



DENSITY AND SPECIFIC GRAVITY. 



Manipulation. — Arrange apparatus as in Fig. G7. Place 
water in one tumbler and in the other the copper sulphate- 

By applying the lips to the 
glass mouthpiece a, suck 
some air out of the bottle 
B, thus causing a column 
of liquid to rise in each 
tube. Without removing 
the mouthpiece from the 
lips, compress the tube 
tightly with the left hand, 
and while holding it in this 
manner, replace the mouth- 
piece by the solid plug 
(which may be covered with 
vaseline). On releasing 
the tube, the columns of 
the liquids will stand at a 
certain height in each. By 
bringing a scale alongside 
the tube, the height of 
each column from the level 
of the liquid may be ob- 
tained. The specific gravity 
fig. 67. is equal to the height of 

the water column divided 

by the height of the other column. Repeat several times 

with different heights. Tabulate result : 




Height of Water. 


Height of other Liquid. 


Specific Gravity. 









Replace the water by some other liquid, and, taking the 



SPECIFIC GRAVITY OF TWO LIQUIDS. Ill 

copper sulphate as the liquid of known density, determine 
the specific gravity of the other liquid. 

Questions. — How does this method differ in principle 
from Exercise 6 ? With sufficiently long tubes, could de- 
terminations of specific gravity be made in this way by 
entirely removing the air ? Suggest a method of determin- 
ing specific gravity based upon Exercise 8. 



HEAT. 



The Bunsen Burner. — The instrument commonly used 
for heating bodies is a burner, called the Bunsen Burner. 
This instrument (Fig. 68) is con- 
nected with the gas-pipe by a rub- 
ber tube, and consists of a pipe, a, 
provided with holes near the bot- 
tom, which can be closed, if desired, 
by turning the sleeve, 8. The gas 
enters the bottom of the tube through 
a small opening, and, when lighted 
at the top of the tube, burns with a 
very hot blue flame, free from smoke. 
On shutting the air-holes, the flame 
becomes yellow and smoky. Never 
fig. 68. use the yellow flame except when 

specially instructed to do it. It will cover with a coating 
of lamp-black whatever is put in it. When turned down 
low, the flame sometimes runs down to the bottom of the 
tube, and burns at the point where the gas enters.* This 
is called " backing-down," and is often indicated by the 
flame taking a green color. Backing-down should be 
stopped at once, as it will make the lamp very hot, some- 
times even hot enough to melt the rubber tube. A smart 
blow of the fist on the rubber tube as it lies on the table 
will often cause the flame to jump to the top of the tube. 
If this fails, the gas must be turned off and relighted. 




* Partially closing the sleeve when tbe gas is turned low tends to 
prevent this. 

112 



BOW BEAT TRAVELS. 113 

Precautions in Heating.— If a flask is nearly full of 
water, it is fairly safe to heat it directly, but care must be 
used that the flame strikes the glass nowhere above the 
level of the water. Test tubes are usually heated directly 
in the flame, w T ith the same precautions. They may be 
held by a strip of paper, doubled three or four times, and 
passed around the tube near the top.* The bottom of 
any vessel to be heated should usually be held about three 
inches above the top of the burner. The safest way of 
heating a glass flask is by means of a shallow saucer of 
sheet-iron, filled with sand, in which the bottom of the 
flask rests. Such an arrangement is called a sand-lath, 
and, when the burner is placed under it, should be sup- 
ported three or four inches above the top of the tube. In- 
stead of a sand-bath, a piece of wire-gauze is often used. 
This is placed upon the ring of the ring-stand, and the 
bottom of the flask allowed to rest upon it. Never place 
your hand where, should the vessel heating break, the hot 
contents can fall upon it. 

EXERCISE 1. 

HOW HEAT TRAVELS. 

Preliminary. — In the following exercise we wish to ob- 
serve what happens when one portion of a body is raised to 

a a a a a a a a a 




a higher temperature than the other portions. "We may 
use the apparatus shown in Fig. 69, which consists of a 

* Essentially as in Fig. 48. 



114 HEAT. 

rod held by the support S, so that one end may be heated 
by the burner BB. Make some pellets of wax a little 
larger than the head of a pin, and place them at regular 
intervals along the upper side of the rod, as aa. Any con- 
siderable rise in temperature at any point on the rod will 
be indicated by the melting of the pellet there. We must 
try several rods of different materials, and vary the condi- 
tions by bringing two different substances in contact, in- 
stead of using different parts of the same substance. Fi- 
nally, we must try a liquid. The case of a liquid is a little 
different, because its particles are free to move among 
themselves, and we shall require some means of observing 
such motion if it occurs. 

EXPERIMENT I. 

Apparatus.— Exp. 1-3. Rod to be heated, with support; wax or 
paraffine; means of heating the rod. Exp. 4. Incandescent lamp 
that can be lighted. Exp. 5. Rods of wood, glass, and iron, with 
means of heating them. Exp. 6. Rod of Exp. 1; thin glass vessel; 
water; means of heating. Exp. 7. Ring-stand; lamp; wire-gauze or 
sand-bath; water; some crystals of potassium permanganate. 

Object. — To observe what happens when one portion of 
a solid is kept at a higher temperature than the rest. 

Manipulation. — The rod being fastened so that the 
end to be heated is about 2 cm. above the top of the Bun- 
sen burner, close the air-holes of the burner, light it, and 
turn off the gas until the flame is about .5 cm. high.* Heat 
one end of the rod with this low flame, and record your 
observations. If possible, note the time at which the melt- 
ing of each piece of wax begins. Write out all you have 
learned regarding what takes place when a portion of the 
rod is kept at a higher temperature than the rest of the 
rod. 

EXPERIMENT 2. 

Object. — To study the distribution of the heat in the 
rod. 

* This gives the yellow, smoky flame. 



HO W HEAT TRA VELS. 115 

Manipulation. — Eemove the burner, and by the fingers 
or any convenient method test the temperature at different 
points of the rod, including the ends. Draw a line to rep- 
resent the rod, and illustrate the distribution of the heat 
by a line drawn around it. 

EXPERIMENT 3. 

Object. — To find if the rod loses heat. 

Manipulation. — Replace the burner, open the air-holes, 
turn on the gas, and heat one end of the rod about two 
minutes. Remove the lamp and bring your hand near, but 
not touching the end that was heated. Does the rod seem 
to be losing heat? Is this loss in every direction? To 
test this latter point, hold the hand about .5 cm. from the 
heated end of the rod, above, below, on either side, and 
horizontally from the end. Write out what you have 
learned regarding the loss of heat. 

EXPERIMENT 4. 

Object. — To observe if the results in Exp. 3 can still be 
obtained in the absence of air. 

Manipulation. — Observe an Edison lamp ; turn on the 
current and see if the heat from the hot carbon reaches 
your hand through the space in the globe from which the 
air has been exhausted. Record your answer to the ques- 
tion. 

EXPERIMENT 5. 

Object. — To find if all bodies behave in a similar man- 
ner when one portion of them is heated. 

Manipulation. — Repeat Exp. 1 with rods of wood, iron, 
glass, etc., recording carefully the results in each case.* 
See if you can class together any substances that behave 
alike in this respect. Record results in tabular form. 

* Or the experiment can be tried by holding one end of the rod in 
the hand, heating the other end in the flame, and observing whether 
the end in the hand becomes heated or not. 



116 HEAT. 

EXPERIMENT 6. 

Object. — To observe what happens when a heated body 
is brought in contact with a cooler body. 

Manipulation. — Place about 50 cu.cm. of water in a 
glass vessel and note the degree of warmth by means of the 
finger. Heat one end of the copper rod for a few moments, 
plunge it into the water, stir it around, withdraw it, and 
again test warmth of the water. State your inference. 

EXPERIMENT 7. 

Object. — To observe what happens when one part of a 
liquid is heated hotter than the rest. 

Manipulation. — Support the thin glass vessel used in 
Exp. 6 on a ring-stand, by means of a wire-gauze ; fill it 
three-quarters full of clean water. Have ready the burner 
turned down low, and adjust the ring-stand so that the 
vessel is supported about 3 cm. above the top of the burner. 
Drop into the water four crystals of the pink substance 
given you (which in dissolving colors the water), and at 
the same instant place the lamp under the vessel. Any 
motion of the liquid will be indicated by the motion of its 
colored portions. Watch carefully and draw a diagram 
representing your observations. Compare as carefully as 
possible the behavior of a solid with that of a liquid when 
one part is heated more than another. 

Definitions. — The process by which heat is transferred 
from one part of a body to another part, or from one body 
to another in contact with it, is called Conduction. The 
process by which a body loses heat when in contact with no 
other body, as in the case of the electric light, is called 
Radiation. The process by which heat is distributed 
through a liquid or gas, as in Exp. 7, is called Convection. 
The condition of a body as regards its ability to give up 
heat is called its Temperature. The body giving up heat 
is said to have the higher temperature. The word "tern- 



TESTING THERMOMETERS. Ill 

perature " is used to indicate the relative degree to which a 
body possesses the property of causing the sensation that 
we call heat. It is always used with reference to the con- 
dition of some other body taken as a point of comparison. 

EXERCISE 2. 

TESTING THERMOMETERS. 

Preliminary. — The fact that bodies expand when their 
temperature is raised and. contract when it is lowered, is 
made use of in constructing instruments to measure changes 
in temperature. These instruments are called thermome- 
ters* They usually consist of some substance so arranged 
that changes in its volume may be observed on a scale. 
The instrument generally used in laboratory work is called 
a chemical thermometer. The substance used is mercury. 
It is contained in a glass bulb connected with a fine tube 
with thick walls. The scale is engraved on the walls, every 
ten degrees being numbered. The centigrade scale is gen- 
erally used. At the top of the instrument is a small glass 
eye by which it may be suspended. Such thermometers 
are usually provided with a case in which they should 
always be kept when not in actual use. The glass of the 
bulb is very thin, and great care should be used not to 
break it. "When a thermometer is used to determine the 
temperature of a liquid, the bulb should not be allowed to 
come in contact with the sides or bottom of the containing 
vessel. When a thermometer has been at one temperature 
and is to be exposed to a very different one, as in changing 
from ice-water to steam, hold it in the air a moment before 
exposing it to the new temperature. For changes of a few 
degrees this precaution is not necessary. In reading a 
chemical thermometer, a white card held behind the glass 
makes the position of the top of the mercury column much 
more distinct. 



118 HEAT. 

After thermometers have been used for a time, the posi- 
tion of the mercury at the temperature of melting ice does 
not always agree with the point on the scale, and some- 
times the position at 100° also changes. Hence the ther- 
mometer used in the following exercises should be tested, 
in order that, if necessary, corrections may be made in its 
readings. The correctness of the point is tested by plac- 
ing the thermometer in melting ice (whose temperature is 
always 0); the 100° point is tested by immersing the ther- 
mometer in steam (whose temperature is known).* 

EXPERIMENT. 

Apparatus.— Thermometer to be tested; ice or snow; water; flask 
and ring-stand, and wire-gauze or sand-bath; tumbler; clamp; deliv- 
ery-tube ; large glass tube 3 or 4 cm. longer than thermometer, corked 
at one end, the cork having a hole for the thermometer and another 
holding a piece of small glass tube for connecting with boiler. 

Object. — To test the correctness of the points on the 
scale of the thermometer which correspond to the temper- 
atures of melting ice and steam. 

Manipulation. — Part I. Place the thermometer in 
the centre of some pounded ice or snow in a tumbler, the 
zero-pointf on the scale being just exposed. Allow it to 
remain there until the mercury has ceased to fall. Kecord 
the point on the scale at which the mercury comes to rest. 
This point is the true zero-point on the scale. 

Part II. Clamp the large tube in a vertical position, 
corked end up. Connect the delivery-tube from a flask 
about two-thirds full of water with the small tube in the 
cork. Thrust the thermometer through the other hole in 
the cork until the 100° point is just above the cork. Boil 
the water in the flask, thus surrounding the thermometer 

* Of course thermometers do not need testing every year or with 
every class. 

f These instructions assume that the thermometer has a centigrade 
scale. 



TEMPERATURE AND PHYSICAL FORM, 119 

with steam, and note the reading of the mercury column 
when it comes to rest. Draw the thermometer up until 
the bulb only is below the cork, and see if it makes any 
difference in the reading whether all the mercury is heated 
or not. Eead the barometer. The temperature of the 
steam corresponding to the atmospheric pressure may be 
calculated by calling the temperature corresponding to 760 
mm. 100°, and adding 1° for each 27 mm. above 760, or 
subtracting 1° for each 27 mm. below. Eecord the ther- 
mometer-reading, the true temperature of the steam, and 
the difference. 

EXERCISE 3. 

TEMPERATURE AND PHYSICAL FORM. 

Preliminary. — We already know that when the tempera- 
ture of a solid is raised sufficiently, the solid changes to a 
liquid, and at a still higher temperature to a gas. That 
is, the physical form of a body is affected by its tem- 
perature. In the following exercise we wish to find 
out all we can about what goes on when a body is 
heated. Lefc us heat a body and note its changes in 
temperature, and also watch for any other changes. Ice 
is a good substance to work with. If we put some ice in a 
vessel, heat it, and note the temperature at regular inter- 
vals, we can see if there is any definite connection between 
temperature and physical form. At the beginning, some 
water must be added to the ice to get the temperature, as 
we could not thrust the thermometer directly into the ice. 
The contents of the vessel must be stirred in order to keep 
the temperature everywhere the same. We can weigh the 
vessel before and after heating to see if there is any 
change in weight. The apparatus used is shown in Fig. 
70. A tin pail supported over the burner B.B. is filled 
with ice and water. The temperature is measured by the 



120 



HEAT. 



thermometer T, and the contents of the pail stirred by 
the paddle P. 




EXPERIMENT. 

Apparat us.— Ring-stand and burner; tin pail: paddle; thermome- 
ter; ice or snow; water; watch or clock; spring-balance or rough 
scales ; test-tube of cold water or plate of clean dr}' glass. 

Object. — To observe the effects of heating a body. 

Manipulation. — Place about 100 cu. cm. of water in 
the pail; add enough ice or snow to fill the pail two-thirds 
full of the mixture ; weigh the pail and contents on the 



TEMPERATURE AND PHYSICAL FORM. 121 

spring-balance.* Eecord the weight. If ice is used, it 
should first be wrapped in a cloth and pounded until it is 
fine. By means of the paddle stir the contents of the pail 
vigorously until the thermometer reads zero. Adjust the 
thermometer so that the bulb is well covered, and does not 
touch the sides or bottom of the pail. Place under the 
pail a very low flame, turning the gas nearly off and 
almost closing the air holes in order to prevent backing- 
down. Stir vigorously, taking care that the solid and 
liquid are thoroughly mixed, and being careful not to 
break the bulb of the thermometer. Note the tempera- 
ture at one-minute intervals until four minutes after the 
water has boiled. The readings must be continuous from 
the beginning to the end of the experiment. When the 
readings are completed, weigh again. From time to time 
during the work hold over the pail a piece of clean dry 
glass, or a test-tube filled with cold water, and observe the 
results. In addition, note all tliat goes on, and record all 
your observations. 

Eecord results as follows : 

Weight before = 

Weight after = 



Time. 


Temperature. 


Remarks. 









Under "Time," place the hour and minute of each 
reading. Under " Temperature," place the thermometer- 
reading to 0.1 degree. Under " Remarks," place any 
observations that you made at the time of the reading. 

* A 64-oz. balance is the best. 



122 



HEAT. 



Note carefully changes of form, appearance, formation of 
bubbles, moisture, etc. 

Questions. — 1. What effect has the addition of heat on 
the physical form of a solid ? 2. What effect has the addi- 
tion of heat on the physical form of a liquid ? 3. Is it 
possible to add heat to a body and not raise its tempera- 
ture ? 4. Under what circumstances ? 5. Under what 
circumstances does the addition of heat raise the tempera- 
ture ? 6. Is any change of weight produced? 7 Why is 
it necessary to stir the mixture ? 8. When the tempera- 
ture rises, is the rise regular ? 



GRAPHIC REPRESENTATION OF RESULTS. 
CURVE PLOTTING. 

Where an experiment includes two sets of measure- 
ments, as the time and temperature measurements just 
made, the results are often expressed by means of a dia- 
gram. Suppose, for example, the following data have been 
obtained : 



Time. 


Temp. 


Time. 


Temp. 


11 h. 3 m. 


5° 


11 h. 23 m. 


4 


5 


7 


25 


3 


7 


4 


27 


2 


9 


3 


29 


4 


11 


3 


31 


5 


13 


5 


33 


6 


15 


8 


35 


5 


17 


6 


37 


4 


19 


7 


39 


3 


21 


5 


41 






To represent these results in a diagram, on a page of 
of your note-book, draw two lines at right angles, as AB 
and BC in Fig. 71. Let BC represent time and AB 
temperature. Divide the line BC into as many equal 
parts as there are observations recorded ; in this case, 18. 



GRAPHIC REPRESENTATION OF RESULTS. 123 

Divide the line AB into as many equal parts as there are de- 
grees between the highest and lowest temperature noted; 
in this case, 8. From each of the points a draw lines 
parallel to BC and equal to it in length, and from the 
points c on BC draw lines parallel to AB, thus dividing 
the paper up into a number of rectangles. Starting at 
the point where the two lines first drawn meet, mark on 



8° 


a — 


I ( 


i c 


I < 


I c 


I 


d , 


I ' 


I c 


I i 


i c 


1 c 


7 I 


I c 


I ( 


I i 


i i 


I ( 


I t 


l b 


:- 


CM 










j 




























b 


6 r 
5~> 








































b 
h 












j 




































j 
































4° 










/ 






























h 






\ 




/ 
































3° 

2° 






\ 




/ 






























h 






































\ 


b 






































\ 




r 

o 








































b 


CD 


', 


- 


1 










i 


1 






J 


i 










\ 



3 

b m 



11 13 15 IT 19 21 23 25 27 



31 33 35 37 



AB the temperature 5, the first observation, by making a 
cross five spaces up the line. Then on the next vertical 
line, which marks the time of the next observation, make 
a cross at the intersection opposite the next recorded tem- 
perature. Proceed in this way until all the temperatures 
have been entered. Connect the centres of the crosses by 
straight lines, or by a regular curve. The line so obtained 
will represent the temperature at various times. By in- 
serting at the proper places on the curve any observations 



124 



HEAT. 



that may be noted as regards changes, etc., a complete 
graphic account of the results of the experiment is ob- 
tained. This process is called curve-plotting, and is much 
used to represent to the eye the results of experiments. 

Taking the results you obtained in the preceding experi- 
ment, plot a curve on one complete page of your note- 
book, representing the changes in temperature during the 
entire experiment. Enter at the proper points of the curve 
any phenomena that may have been observed. A curve 
like this is often called a temperature-curve. If BC be 
drawn the long way of the note-book page, the blue-ruled 
lines will be convenient for the vertical lines. The hori- 
zontal lines should be ruled very lightly with a pencil. 
Evidently any standard of length can be used in laying off 
the spaces. In Fig. 71, 1 cm. on the line BC represents two 
minutes of Time, and 2 cm. on the line AB represent one 
degree of Temperature if AB — 16 and BC — 19 cm. 

EXERCISE 4. 

LAWS OF COOLING. 
EXPERIMENT. 

Apparatus.— A small beaker-glass; thermometer, and clamp to 
support it; watch or clock ; tin pail; water; ring-stand; and burner 
for heating the water. 

Object. — To observe the change in temperature in a 
cooling body. 

Manipulation. — Place about 50 cu. cm. of hot water in 
a beaker glass, suspend the thermometer in the liquid, and 
observe the temperature every minute for twenty minutes. 
Every five minutes also observe the temperature of the 
room. Record results as follows: 



Temp. 


Time. 


Temp, of Room. 


Weight used. 











Repeat with 25 cu. cm. of water. 



MELTING AND BOILING POINTS. 125 

Questions. — 1. What have you observed regarding the 
changes in temperature when a body cools ? 2. Does the 
quantity of the body make any difference ? 3. Plot curves 
showing the changes in temperature in each case. 4. Does 
the difference in temperature between the body and the air 
seem to affect the rate at which the temperature falls ? 

EXERCISE 5. 

MELTING AND BOILING POINTS. 

Preliminary. — In the following exercise it is desired to 
observe the melting-points of some solids, and the boiling- 
points of some liquids. The melting-point of a solid is 
usually determined by immersing a small portion of it in 
some liquid having a sufficiently high boiling-point, heating 
the liquid, and noting its temperature when the solid melts. 
For bodies which it is supposed will melt below 100°, water 
is used; for higher melting-points, other liquids. The 
solid is usually placed in a small tube, called a 
melting-tube, which is attached alongside the ther- 
mometer. A melting-tube is made by drawing out 
a piece of glass tubing in the flame of a Bunsen 
burner, as shown in Eig. 72. The tube should be 
about 10-15 cm. from the narrow neck to the upper 
end, and the small part about 3 cm. long. Melt 
some of the solid (paraffine, for instance) in a 
small dish, draw a little up into the tube, and 
after wiping the outside allow it to cool. In 
determining the boiling-point of a liquid, a test- fig. 72. 
tube, containing about 1 cu. cm. of the liquid takes the 
place of the melting-tube. 

EXPERIMENT 1. 

Apparatus.— Ring-stand; sand-bath and burner ; thermometer, and 
some means of supporting it; "melting-tubes;" wax or paraffine in 
small dish (if tubes are unprepared); water; stirring- rod; rubber 
bands. 

Object. — To determine the melting-point of a solid. 
Manipulation. — Attach the tube containing the solid 



126 



HEAT. 



to the thermometer by elastic bands or strings, as indicated 
in Fig. 73, the solid being on a level with the thermometer 
bulb, and support the whole so that the bulb is about in 
the centre of the dish of water. Heat the water slowly, 
stirring gently, and note the temperature either when the 
solid becomes transparent, or when it slides up the tube. 
Either of these may be taken as indicating the melting- 
point. The second gives a little higher temperature than 
the first. Add some cold water, and repeat with a fresh 
tube. If possible, try more than one substance. 









y=r=^ 


i!i^= 


— 


^~ .: 


— 


— _ 


; - : 






\ = = 




— : 









E 


— 






|Lz=_- 


— 


\— /- 




i 





J 


— — 




~) 















EXPERIMENT 2. 

Object. — To determine the boiling-point of a liquid. 

Manipulation.— Place about 1 cu. cm. of the liquid in 
a test-tube and support the tube in the beaker, which has 
been filled with cold water, so that the liquid is in the 
centre of the water, as in Fig. 74. Warm the water slowly, 



HEAT CAPACITY. 127 

stirring gently with the thermometer, and note the tem- 
perature at which the liquid begins to boil. It is best to 
shake the tube gently while heating. Make two deter- 
minations with one liquid, and, if possible, repeat with 
another liquid. Alcohol, ether, etc., are very inflammable, 
and should be kept away from the fire. 

EXERCISE 6. 

HEAT CAPACITY. 

Preliminary. — In the following exercise we wish to study 
the conditions affecting the rise in temperature of bodies 
when heated. We already know that the longer a body is 
heated, the more its temperature rises,* provided no change 
of form takes place, and that the greater the difference in 
temperature between the source of heat and the body, the 
more rapid will be the change.f In the following exercise 
we wish to see if the nature and quantity of the body 
heated have any effect. \ 

EXPERIMENT. 

Apparatus.— Part I: Test-tube, with perforated cork; thermom- 
eter; tin pail; ring-stand; burner; water; scales and weights ; a bu- 
rette or graduated cylinder. 

Part II.: Three test-tubes with corks; mercury; alcohol; empty 
tumbler; also the apparatus for Part I. 

Object. — To observe the effect on the rise of tempera- 
ture in a body produced by (a) quantity, (b) material. 

Manipulation. — Part I. Effect of Quantity : — Place 4 
grams of water in the test-tube, close the mouth of the tube 
by a cork through which the thermometer passes, the bulb 
being immersed in the liquid. Have ready the large vessel in 
which the water is boiling, place the tube in the water, stir 
it gently, and observe the time required for the thermom- 

* Ex. 3. f Ex. 4. 

X Let each pupil prepare a statement of the conditions under which 
such an exercise must he conducted. 



128 



HEAT. 



eter to rise 10 degrees. Repeat the experiment with twice 
the weight of water. 

Part II. Effect of Material: — Weigh out in three tubes 
15 grams, respectively, of water, mercury, and alcohol. 
Cork the tubes, and stand them upright in an empty 
tumbler until ready for use. Take the tube containing the 
water and substitute for its cork the one bearing the ther- 
mometer. Having the thermometer bulb immersed in the 
water, read the temperature of the liquid and then plunge 
it into the boiling water. Shake it gently, and observe the 
time required for the thermometer to rise 2 degrees. Re- 
peat the experiment with the other liquids. Tabulate the 
results as follows : 



Wt. used. 


Original Temp. 


Final Temp. 


Time of Immersion. 


Body. 













Questions. — 1. For a given substance, can you make 
out any relation between the rise of temperature and the 
weight used ? 2. Will exposure to the same temperature 
for the same time cause the same rise in temperature in all 
bodies ? 

EXERCISE 7. 

DETERMINATION OF SPECIFIC HEAT. 

Preliminary. — We observed in the preceding experiment 
that when equal weights of various bodies were exposed to 
the same temperature for the same time, the temperature 
of some rose more rapidly than that of others. This is in- 
dicated by saying that they have different heat capacities. 
The lower the heat capacity, the higher the temperature 
rose; and the less the temperature rose, the greater the 
heat capacity. Which has the greater heat capacity — water 
or mercury? 



DETERMINATION OF SPECIFIC HEAT 129 

The unit of heat quantity is the heat required to raise a 
unit of weight of water from to 1° on a temperature scale; 
hence the quantity of heat taken by any quantity of water 
is found by multiplying the weight of the water by its rise 
in temperature, or 

H = W X Rise in temp. 

Evidently we can have several units of heat, according to 
the unit of weight taken and the thermometer scale used. 
The units of weight generally used are metric, the kilo- 
gram and the gram, and the scale used is the centigrade. 
The corresponding unit of heat is called the calorie. When 
kilograms are used the calorie is designated by a capital C; 
when grams are used, by a small c. 

In order to be able to use these heat-units for all bodies, 
we must compare their heat capacities with that of water, 
which is taken as the standard. This comparison is ex- 
pressed as the ratio of the heat capacity of the body to 
that of water, and this ratio is called the Specific Heat 
of the body. As the specific gravity of a body expresses 
how many times its density is that of water, so the specific 
heat of a body expresses how many times its heat capacity 
is that of water. 

The simplest way to determine specific heat would be to 
take equal weights of water and the body to be tested, 
expose them for the same length of time to the same tem- 
perature, and note the rise of temperature. The higher 
the temperature of the body rose, the less would be its heat 
capacity. If, for example, the temperature of the body 
rose twice as much as that of the water, its capacity would 
be half as much, and its specific heat one half; if it rose 
half as much, its specific heat would be 2, etc. Calculate 
from the data of the preceding exercise the specific heat 
of mercury. 



130 HEAT. 

Specific heat is usually determined by what is called the 
"method of mixture." This consists in heating the body 
to a known temperature, and then bringing it in contact 
with water in a vessel, called a calorimeter, which will not 
lose heat by radiation. The body will lose heat and the 
water will gain it, until both are at the same temperature. 
Then the quantity of heat gained by the water will equal 
the quantity of heat lost by the body. If we know the 
weight of water in the calorimeter, and how many degrees 
it was raised, we can calculate how much heat was gained 
by the water, or, the equivalent, that lost by the body. If 
we also know the weight of the body, and the number of 
degrees it cooled, we can determine how many heat-units 
would be given out by one gram of the body cooled 1°. 
Dividing this by the amount of heat that would be given 
off by one gram of water cooled 1°, we can get the specific 
heat. In the following exercise we use an iron ball of 
known weight, heated in boiling water to 100°. Taking a 
known weight of water and noting the rise in temperature, 
we calculate the specific heat. 

EXPERIMENT. 

Apparatus.— Body whose specific heat is to be determined. Tin 
pail; ring-stand and burner; water; thermometer with white card; 
scales and weights ; calorimeter; three corks; thread. 

Object. — To determine the specific heat of a given solid. 

Manipulation. — Fill the pail about three-fourths full 
of water, and light the burner under it. Weigh the calo- 
rimeter, fill it about two -thirds full of water,* and weigh 

* The point is not to get so much water in the calorimeter that it 
will overflow when the body is put in, but yet to have enough to 
completely cover it. A preliminary trial may be needed. Place the 
body in the calorimeter, and then add water enough to rill the calo- 
rimeter to about 5 cm. of the top. On withdrawing the body, the 
amount of water for good working conditions remains, and may be 
weighed. 



DETERMINATION OF SPECIFIC HEAT. 131 

again. Support the calorimeter on the corks upon the 
table at some distance from the heating apparatus, and put 
the thermometer into it. Weigh the solid under examina- 
tion. When the water in the pail boils, suspend the solid 
in the centre by means of a thread, and allow it to remain 
there until it has assumed the temperature of the water 
(100° approximately). This will take about four minutes. 
Then read the thermometer and quickly transfer the solid 
to the calorimeter. Stir gently with the thermometer 
and read it to 0.2 at intervals of half a minute (record 
these readings) until the temperature of the water begins 
to fall. The highest reading of the thermometer is the 
temperature to which the solid heats the water. If time 
allows, repeat with different quantities of water in the 
calorimeter. Record results as follows : 

Weight of body = 

Calorimeter -f water = 
Calorimeter alone = 



Water alone = 

Temperature of body before immersion = 

" " water in cal. after body is in = 
" " " " " before body was in = 

Increase in temp, of water in calorimeter — 

Fall in temp, of body = 

Questions. — Explain why the space between the walls 
of the calorimeter is filled with excelsior. Suggest some 
other substances that would do as well. Why should the 
solid be suspended by a thread rather than by a wire? 
What error is introduced by doing so ? What error is in- 
troduced in calling the original temperature of the ball 
100°? 



132 



HEAT. 



Calculation.— Call the weight of the body W and the 
weight of water in the calorimeter W, the original tempera- 
ture of the water t and the final temperature V. Then W 
grammes of the body in cooling from 100° to t' degrees 
gave off sufficient heat to raise W grammes of water from 
t degrees to t' degrees, or raised it t' - t degrees; the 
amount of heat given up was 

w x ? - 1. 

As the heat was given up by IF grammes of the body cooled 
from 100° tot — t' degrees, the amount of heat given out 
by one gram cooled one degree was 

Wxt'-t 



W X 100 - t' 
Since this also represents the amount of heat that would 
be required to raise one gram of the body 1°, we can get 
the specific heat of the body by dividing this value by the 
amount of heat that would be required to raise 1 gram of 
water 1° or lc; so 

W Xt'-t 

Specific heat=^ Xl00 -^ 
lc 

By substituting in this equation the values obtained in the 
experiment, the specific heat of the body may be calculated. 
In this calculation we have neglected to take into ac- 
count the heat that went into the calorimeter, which was 
itself heated. To make this correction, weigh the vessel 
that formed the inside of the calorimeter.* This gives 
the weight which was heated from the original tempera- 
ture of the water to its final temperature, or t' — t; and 
so the heat that went into the calorimeter = Wt. cal. x V 
— t X the specific heat of the material of the calorimeter. \ 

* Or, if a metallic calorimeter be used, weigh the whole vessel, 
t Glass, 0.198; brass, 0.858; iron, 0.1124. 



LATENT HEAT. 133 

The total heat given out by the body equals that which 
went into the water plus that which went into the calorim- 
eter. The corrected formula, then, would be: 

Specific Heat = 

(W X f - t) + (wt. cal. X t' — t x sp. heat of cal.) 

W X (100 - t') 

\c 

Re-calculate your value for specific heat with the correction 
for the calorimeter. 

EXERCISE 8. 

LATENT HEAT. 

Preliminary. — The name latent heat is given to the heat 
which is required to change a solid to a liquid, or a liquid 
to a gas, without altering its temperature. Latent heat 
is usually determined (1) by measuring the heat given 
out by a known weight of vapor at the boiling-point of 
the liquid when condensed at that point, or (2) by deter- 
mining the heat absorbed by a known weight of the solid 
at the melting-point when changed to a liquid at that tem- 
perature. In this exercise, the number of heat-units given 
off by one gram of steam at 100° when changed to water at 
that temperature is to be ascertained. The steam is con- 
densed under such conditions that the heat given off will 
raise the temperature of a known weight of water. If we 
know the weight of steam condensed, the weight of water 
heated, and the number of degrees that it was raised by the 
condensed steam, we can calculate the latent heat. 

The apparatus used in the first method consists of a glass 
vessel D, Fig. 75, holding the water, and containing a glass 
coil E, which terminates in a tube that projects from the 
bottom of the vessel. This coil is connected by the tube C 
with the flask A, which furnishes steam. iTis an arrange- 
ment to prevent any condensed steam from passing into 



134 



HEAT. 



the coil. The tube G is thickly wound with cloth to stop 
any loss of heat and resulting condensation of steam before 
reaching E. When steam from A reaches E it condenses, 




and so raises the temperature of the water in D. The con- 
densed steam runs out into a vessel, and the weight of 
water so formed gives us the weight of steam condensed. 

EXPERIMENT 1. 

Apparat us.— Ring-stand; wire-gauze; burner; small beaker-glass; 
scales and weights; thermometer; liter and half liter flasks; paddle; 
apparatus as in Fig. 75. 

Object. — To determine the number of heat-units re- 
quired to change one gram of steam at 100° to water at 
100°. 

Manipulation". — Fill the flask A about two-thirds full 
of water and set it to boiling, the delivery-tube being dis- 
connected at H. Place a measured quantity of water in 
D * (2 to 4 liters, according to size), and suspend the ther- 

* The object, of course, is to get a known weight of water in D. 
This could be done by weighing D, tilling it with water, and weigh- 
ing it again. It is much more convenient, however, to measure the 



LATENT HEAT. 135 

mometer in the liquid. As 1 cu. cm. of water = 1 gram, 
you now know the weight of water in D. Weigh the small 
glass vessel F. When "live steam" comes out of the de- 
livery-tube at H, connect it with the glass coil and allow it 
to run for three minutes, meantime stirring the water in 
D with the paddle.* Read the temperature of the water 
in D, and immediately place the small glass vessel under 
the end of the glass coil to catch the distilled water. Let 
the apparatus run from 15 to 20 minutes, stirring the 
water in D gently all the time; then remove the glass ves- 
sel containing the condensed steam, and immediately read 
the temperature of the water in D. Disconnect the steam- 
pipe and turn out the gas under A. Weigh the vessel 
containing the condensed steam. Arrange the results as 
follows: 

Water in the condenser == 

Original temperature = 

Final temperature = 



Rise in temperature = 

Vessel -f- condensed steam = 
Vessel alone = 



Weight of steam condensed = 

Calculation. — Call W the weight of water in the con- 
denser, W the weight of steam condensed, t the original 
temperature of the water in D, and t' the temperature to 
which it was raised. Then W X (t' — t) = the heat gained 

water. It is best to fill B within about 5 cm. of the top, and it is 
convenient to take a volume which can be measured by liter or 
half-liter flasks. 

* In stirring, care should be used not to break the glass coil, and 
to continually stir the water up from the bottom, at which point the 
colder water will always collect. The thorough stirring of the water 
is an important point all through the experiment. 



136 HEAT. 

by the water in D during the experiment. This amount of 

heat includes not only the heat given out by the steam at 

100° when condensed to water at 100°, but also the heat 

given out by the water so formed in cooling from 100° to 

the temperature of the water in D, which varied from t 

degrees at the beginning to t' degrees at the end of the 

experiment. The average temperature to which this water 

t' — t 
was cooled was — - — • and the amount of heat given off by 

the water formed from the steam in cooling was * 

W x (ioo - *-=-*). 

So that the heat gained due to the condensation of steam 
alone is 

Wx (*' -t)- [V x (ioo - 1 -^)\ 

and the amount of heat per gram is 

Wx (f -t)W X 100-^-=-? 



W 

There are two errors that still need correcting for, if the 
results are to be at all accurate. (1) The glass vessel D 
and the glass coil E are raised from t degrees to V degrees, 
as well as the water inside; hence the value taken for the 
heat given out is too small by the amount that went into 
the glass. To correct for this, weigh D and the coil to- 
gether. Calling this weight G, the heat that went into the 

* The original temperature being 100°, the average fall in tempera- 
ture would be 100° — . 



LATENT HEAT. 



137 



glass is G X (f — t) X specific heat of glass.* If this 
quantity be added to the value taken before for the heat 
given up to D, it will give more accurate results. (2) Dur- 
ing the experiment the water in D was losing heat to the air 
in the room.f This error can be avoided by filling D with 
water a number of degrees below the temperature of the 
room.J and stopping the experiment when it is heated as 
much above the temperature of the air as it started below. 
Then the water in D takes as much heat from the air while 
below its temperature as it gains while above, and so this 
error cancels out. The corrected calculation, then, is 

Latent Heat = 

[Gx(t'-i) Xsp. beat steam] + [Wx(t'-t)] -\ Wx (lOO- 



32 



W 
SUBSTITUTE EXPERIMENT. 

Preliminary. — The apparatus is shown in Fig. 76. Steam 
is generated in the flask, and passes through the covered 
tube into the calorimeter contain- 
ing a known weight of water. The 
temperature of this water is ob- 
served before and after running in 
steam, and the increase in weight of 
the calorimeter gives the weight of 
steam condensed. The tube is cov- 
ered with cloth to prevent conden- 
sation. The calorimeter is sup- 
ported on a block or box, so that 
by removing the support, the calorimeter can be quickly 

* This may be taken as 0.198. 

f For another method of correcting for this error, see Worthing- 
ton, p. 190. 

% This can usually be done by taking water from the faucet after 
letting it run awhile, where there is a water service; otherwise, a 
little ice or snow maybe added. 




138 HEAT. 

dropped down so as to clear the end of the delivery-tube 
without disturbing the flask. 

Apparat us. —Ring-stand; wire-gauze; burner; flask with cork 
and delivery-tube; scales and weights; calorimeter and thermom- 
eter with white card; support for calorimeter (books, block of 
wood or small box). 

Object. — To determine the amount of heat given out 
by one gram .of steam at 100° in condensing to water at 
100°. 

Manipulation. — Weigh the vessel to be used as a calo- 
rimeter, add about 300 cu. cm. of water, weigh again, and 
place the thermometer in the vessel. Fill the flask two- 
thirds full of water and heat. After the steam has escaped 
freely from the delivery-tube for three or four minutes, note 
the temperature of the water in the calorimeter, and as 
quickly as possible plunge the delivery-tube nearly to the 
bottom of it. While the steam is condensing, stir gently 
with the thermometer, noticing the temperature from time 
to time. When the temperature of the water in the calo- 
rimeter is 8° or 10° above that of the room, withdraw the 
delivery-tube as rapidly as possible, and remove the lamp 
from beneath the flask. Note the temperature of the water 
in the calorimeter, and weigh the latter. Eecord the re- 
sults as follows: 

Calorimeter -}- water = Steam condensed = 

" = Temp, before = 

Water r= Temp, after = 

Calorimeter -f- water after = Gain in temp. = 
Calorimeter -j- " before = 

EXERCISE 9. 

COEFFICIENT OF LINEAR EXPANSION. 

Preliminary. — We know that when a body is heated it 
expands. The fraction of its length at that it expands 



COEFFICIENT OF LINEAR EXPANSION. 



139 



when heated 1° is called its coefficient of linear expansion, 
or the linear coefficient of expansion. The fraction of its 
bulk at that it expands when heated 1° is called its coeffi- 
cient of cubical expansion, or the cubical coefficient of expan- 
sion. Evidently fluids would have no coefficient of linear 
expansion, but solids would have both.* In the following 
exercise we wish to determine the average linear coefficient 
of a metallic rod. 

First Method. The apparatus is shown in Fig. 77. The 
rod c is surrounded by a large tube ee, which is first filled 
with ice-water and then with steam, thus heating the rod 




100°. The changes in length are magnified by the lever 
p, which reads on the scale S. In this way we can meas- 
ure the change in length of the rod when heated from to 
100° and determine the required coefficient. 



* Suggestion: Give the principles on which such measurements 
would be based. 



140 HEAT. 



EXPERIMENT 1. 

Apparatus.— As shown in Fig. 77. Also, water; ice; funnel; tin 
pail; meter-stick; flask; ring-stand; burner; connecting tubes. 

Object. — To determine the linear coefficient of expan- 
sion of a solid. 

Manipulation. — The chief error in this experiment is 
in the determination of length, since only the part of the 
rod inside the corks is at exactly the measured tempera- 
tures, though the rest of it becomes heated by conduction 
and expands to some extent. If we take the length be- 
tween the outsides of the corks, we shall come very near 
the truth. 

To get the length at zero. Attach the glass funnel to 
the rubber tube L, place a vessel under the exit-tube K, 
and pour ice-water through the apparatus until the ther- 
mometer T has read zero for several minutes. Kead care- 
fully the position of the pointer on the scale, and measure 
the length of the rod between the outsides of the corks. 
Allow the water to run out. Connect with the flask F, 
and run steam through the apparatus until the pointer 
again comes to rest; then note its position. If time allows, 
again pour ice-water through, and see if the pointer comes 
back to its first position. If so, repeat the experiment; if 
not, record the fact. 

To find increase in length. By means of compasses, 
measure carefully the distance between the two pivots, re- 
peating several times, and recording each measurement. 
Measure also the distance from the lower pivot to the point 
on the needle at which you took your reading. The aver- 
age length of the "long arm" divided by the average length 
of the " short arm" gives the magnifying-power of the 
pointer. Record results as follows: 

Length of rod = 

Mag. -power of the pointer = 



COEFFICIENT OF LINEAR EXPANSION. 141 
TABLE OF MEASUREMENTS. 

1st Trial 2d. 3d. Av. 
Short arm, 
Long arm, 

Magnify ing-power = 

Reading pointer at = 
" 100 = 

Increase on pointer = 

True increase = 

Coefficient = 

Calculation. — Snbstract the smaller reading of the 
pointer from the larger; this gives the space traversed 
by the pointer. This, divided by the magnifying-power of 
the pointer, gives the true increase in the length of the 
rod. This increase, divided by the length of the rod at 
zero, gives the coefficient of linear expansion as a decimal 
which is to be carried out to the fourth place of significant 
figures. Or, calling L the length of rod at 0, M the mag- 
nifying-power of the pointer, 8 the reading of the pointer 
at 0, S' the reading of the pointer at 100, 

Increase, 100° = 

Increase, 1° = 

Linear coefficient of expansion = 



Second Method. The apparatus used is shown in Fig. 
78. The rod is inside the tin jacket R, which can be filled 



8' - 8 




M ' 




8' -8 




Mx 100' 




S'- 


-8 


QBlon -Jfx 


100 



142 



HEAT. 



with either steam or ice-water, thus changing the tempera- 
ture of the rod 100°. For measuring the increase in 
length, the pointer P, moving on the clock face, is 
attached to a screw, D, which advances a known distance 
for each turn. The end of this screw is in line with the 
end of the rod, and the screw is connected with one wire 




leading from a source of electricity, while the rod is con- 
nected with the other wire. When the end of the screw 
touches the end of the rod the circuit is completed, and 
this fact is indicated by some instrument placed in the 
circuit. If we know how far the screw advances at one 
turn, the change in length of the rod may be very accu- 



COEFFICIENT OF LINEAR EXPANSION. 143 

rately measured by finding how many turns of the screw 
move its end enough to make contact with the end of the 
rod first at and then at 100°. 

EXPERIMENT 2. 

Apparatus— As shown in Fig. 78. Also, ice-water; tumbler; meter- 
stick; boiler, burner, and ring stand; current of electricity and some 
instrument to indicate when the circuit is completed (galvanometer; 
lamp; sounder). 

Object.— To determine the linear coefficient of expan- 
sion of a metallic rod. 

Manipulation.— Arrange the apparatus as in Fig. 78, 
connecting the glass vessel V with the jacket R, as 
shown. Turn the pointer, P, until the end of the screw, 
D, is just in contact with the end of the rod. Place a 
vessel* under the end of the exit-tube, fill V with ice- 
water, and allow it to run through the jacket, thus sur- 
rounding the rod with water at 0. As the rod contracts, 
turn the pointer so as to just keep contact between the end 
of the screw and the end of the rod, and continue until 
there is no further change in length. During this time 
keep ice-water constantly running through the jacket. 
When the rod has ceased to contract, read the position of 
the pointer at which the end of the screw just touches the 
end of the rod, and turn the pointer back half a revolu- 
tion or so. Replaced by a flask two-thirds full of water, 
and connect it with the jacket R. With a Bunsen burner 
heat the flask and pass the steam through the jacket. 
During this operation turn the pointer back as fast as 
contact is made by the expansion of the rod. The expan- 
sion will be very rapid. When the rod has ceased to ex- 
pand, note the position of the pointer at which contact is 
just made, and record the total number of minutes on the 

* When this vessel is full, the contents are to be poured back into 
V. It is well to have a little ice in it to hold the temperature of the 
water at 0. 



144 HEAT. 

clock face which the poiuter was turned back from its po- 
sition when the rod was at 0. This number, multiplied by 
the decimal of a millimeter which the end of the screw 
moves for 1 minute on the scale, gives the increase in 
length of the rod when heated from to 100°. Again at- 
tach the glass vessel V, run in ice-water, cool the rod to 
0, and ascertain the number of minutes on the scale which 
the pointer must be turned to get contact again. These 
numbers should be very nearly the same. Average them, 
and calculate the coefficient of linear expansion of the rod 
for 10 cu. cm., taking for the length of the rod the dis- 
tance between the outer ends of the jacket corks. Ar- 
range results as follows: 

Reading pointer at = min. 

Pointer moved " 

Reading pointer at 100 = " 

Pointer moved in cooling " 

Average = 

Calculation. — Call the length of the rod L, the num- 
ber of minutes that the pointer moved m s and the distance 
screw moved for 1 m., a. 

Then the increase for 100° = 
and the coefficient for 100° = 



and the coefficient for 1° = 



m 


X 


a, 


m 


\ 


a 




L 


> 


m 


X a 


L 



100 



CUBICAL COEFFICIENT OF A LIQUID. 145 

EXERCISE 10. 

CUBICAL COEFFICIENT OF A LIQUID. 
EXPERIMENT. 

Apparatus.— Alcohol of known specific gravity ; test-tube with 
perforated cork, and glass tube, with scale; tin pail; ice-water; 
ring-staud ; lamp ; thermometer. 

Object. — To determine the cubical coefficient of expan- 
sion of alcohol. 

Manipulation". — Put some ice and water in the tin pail, 
and while the mixture is cooling weigh the test-tube with 
the cork and small tube. Fill the test-tube nearly full of 
alcohol and crowd the stopper in tight, thus forcing a col- 
umn of alcohol up the small tube. This column should 
not be over -4 or 5 cm. high, and no air-bubbles should re- 
main in the test-tube. Weigh again. The increase in 
weight represents the weight of alcohol in the apparatus. 
The volume is found by dividing this weight by the specific 
gravity of the alcohol (marked on the bottle from which it 
was taken). Immerse the test-tube iu the ice-water, allow 
it to remain there until the alcohol column has come to 
rest, and note the position of the top of the column on the 
scale. Remove the ice and slowly heat the contents of the 
pail, stirring gently with the thermometer until the alcohol 
column has risen four or five cm. Stop heating, and note 
when the alcohol column ceases to rise. Read its position 
on the scale, and at the same time note the temperature 
of the water. You have now the distance which the al- 
cohol rose in the tube when heated from to the final tem- 
perature of the water in the pail. 

Calculation. — To determine the increase in volume, 
multiply the rise on the scale by the volume corresponding 
to a rise of 1 cm. as given on the card attached to the in- 
strument. This gives the increase in volume. Record re- 
sults as follows : 



146 BEAT. 

Weight of apparatus + alcohol 
" " " empty 

" " alcohol 
Volume of alcohol 
Alcohol column read at 



No. of degrees alcohol was heated = 
From the data, calculate the cubical coefficient of alcohol 
for 1°. 

EXERCISE 11. 

COEFFICIENT OF EXPANSION OF A GAS AT CONSTANT PRESSURE. 

EXPERIMENT 1. 

Apparatus. — The special form in Fig. 79 ; ice or snow-water ; tin 
pail ; ring-stand ; thermometer ; meter-stick. If apparatus is not 
calibrated there will be required in addition : scales and weights ; 
mercury ; small vessel for weighing mercury ; burette or balances 
that can weigh 300 to 400 grams. 

Object. — To determine the coefficient of a gas under 
constant pressure. 

Manipulation. — To find the volume of the gas used. 
Having no water in B, Fig. 79, remove the gas-holder A, 
and by means of a burette determine its volume in cu. cm.* 
Dry, and place inside B, as shown, and connect with the 
tube DC when full. The volume of gas under test is 
really that in A plus a little in the tube ; but since the cork 
occupies some room in A, it will be near enough to the 
truth to call the volume that of A alone. Fill B with 
water to about 3 in. above the level of A ; add some ice or 
snow. In a short time the temperature of the liquid 
should be 0°. While it is cooling, find the volume repre- 
sented by 1 cm. on the tube D C. Detach the tube at E, 
and draw a column of mercury into it. Lay the tube on a 

* Or, weigh A empty and then full of water. From the weight of 
water contained in A, calculate the volume. 



COEFFICIENT OF EXPANSION OF A GAS. 147 



scale and measure the length of the column. Call this 

length L. Weigh a small dish; pour into it the mercury 

from the tube ; weigh the whole, and compute the weight 

of the mercury alone. Call this weight W. 

Then if J* = specific gravity of mercury, f 

the number of cu. cm. contained in length 

W 
L is -r, and the volume in the tube, per 



W 
cm. of length, = —-. 



Put this down, b 

labelled "Volume per cm. in tube." It 
is best to repeat this several times and 
use the average values obtained. 




Next, draw a small globule of mercury about 1 cm. long J: 
into the tube, and get it near E by gently inclining the 
tube and keeping the finger over one end. This is used as 
an index. Attach the tube at E, and read the position of 
the inner end of the index on the scale F. Before reading 
it is advisable to tap gently with a pencil on the tube over 
the index, as the index is liable to catch a little. If now 
the water in B is at 0°, add a little warm water to it, and 
stir thoroughly with the thermometer until a rise of one or 
two degrees in temperature takes place. As the gas in A 
increases in bulk the index will move out on the scale. 
When the index has assumed a constant position after tap- 
ping, and the thermometer is also constant (at ^°), the dis- 



* This sign is called delta. 
f Say 13.6. 

\ The tube must be dry, and also the mercury, 
end of the meniscus, 



Read from the 



148 



HEAT. 



tance moved by the index represents the increase in volume 
A of a cu. cm. of gas heated from 0° to t°. From these data 
calculate what decimal of its bulk at a gas increases per 
degree centigrade. Put this down, carried out to the 
fourth decimal place, and label it " Coefficient of Expan- 
sion." Add ice to B, and repeat experiment several times 
with different temperatures (t°). Record results as follows : 

Volume of gas taken = 
Vessel weighed = 



Trial. 


Length Mercury Col. 


Wt. Mercury Col. 


Vol. 


Vol. per Cm. 













Average volume per cm. = 

TABLE II. 



Index read 
atO. 


Index read 
aU° 


Distance 

moved by 

Index. 


Volume 
corresponding 


Coefficient of 
Exp. for 1°. 













Average value of coefficient = 

A Second Method. The apparatus is shown in Fig. 80. 
The tube k is closed at one end, and contains a drop of 
mercury, g, to serve as an index. The air whose expansion 
is to be measured is contained between the closed end of 
the tube and the index. This tube passes through a cork 
in one end of a larger tube, act, which is provided with an 
inlet tube T f , and an outlet tube T. The gas can be 
cooled to 0° by filling the large tube with ice-water, and 



EXPANSION OF A GAS AT CONSTANT PRESSURE. 149 

heated to 100° by running in steam. By measuring the 
movements of the index, the coefficient may be calculated, 
as in the preceding experiment. 



EXPERIMENT 2. 

Apparatus.— Special form as shown in Fig. 80. Flask and con- 
nections; ring-stand; gauze and burner ; ice- or snow-water; funnel, 
and vessel to hold ice-water; meter-stick. 

Object. — To determine the cubical coefficient of expan- 
sion of a gas at a constant pressure. 

Manipulation. — Kun steam into the large tube aa. 
As the index is forced out, push the tube in, keeping the 
inner end of the index just inside the outer edge of the 
cork. When the index remains stationary after tapping 
with a pencil, measure the distance from the inner end of 
the index to the outer end of the tube. Disconnect the 
steam, allow the apparatus to cool for a moment, and then 
connect the large tube with a funnel, and run ice-water 
through until the index again comes to rest, when kept 
just outside of the cork as above. After tapping again, 
measure the distance from inner end of the index to the 
outer end of the tube. Eemove the tube and measure the 
distance from its open end to the inner side of the closed 
end. Record results as follows: 

Dist. index from end of tube at 100° = 

a a a a a a a qo _ 



Index moved 
Length of tube 



150 HEAT, 

The length of the tube minus the distance of the index 
at from the open end gives the length of air-column 
used. 

Calculation. — The length of the air-column at 0° rep- 
resents the volume used, and the distance the index moved 
represents the increase for 100° ; so 

Increase 



Coefficient = 



Vol. at (T X 100 



EXERCISE 12. 

ABSORPTION AND RADIATION. 

Preliminary. — We know that when a heated body loses 
heat by radiation, bodies near it are warmed. In the fol- 
lowing exercise we wish to study some of the conditions 
affecting the rate at which heat is absorbed by bodies when 
exposed to radiation. Under what conditions must tests 
be conducted ? What conditions might affect the amount 
of heat absorbed by a body ? 

In the exercise we will use an iron ball to radiate heat, 
and keep it hot with a flame. To absorb the heat, we will 
use tin cans containing water. The cans are of the same 
size, but differ in character of surface — as rough or bright, 
in color, etc. The ball is suspended over the flame and 
the cans supported on blocks, as shown in Fig. 81. 

EXPERIMENT. 

Apparatus.— Part I : Ring-stand; iron ball and wire; two flat tin 
cans of the same size, one covered with lamp-black, each with a 
hole in the cover; blocks of wood to support the cans; two thermom- 
eters ; watch or clock ; water. 

Part II : In addition to the above, tin pail for heating some water. 

Object. — To investigate the effect of color, character of 
surface, etc., on the amount of heat absorbed or radiated 
by a body. 



APSORPTION AND RADIATION. 



151 



Manipulation. — Part I. Suspend the ball by means 
of a wire about four inches above the Bunsen burner and 
light the burner. Fill each can two-thirds full of water, 
put on the covers, insert the thermometers through the 
holes, and support the cans at equal distances from the 
ball and on opposite sides, as in 
Fig. 81. Read the thermometers 
at intervals of a minute for four 
or five minutes. The cans are 
best placed with their largest flat 
sides towards the ball, and great 
care must be taken that the flame 
is equidistant between the two. 
Avoid any draught. 

Part II. Fill both cans with 
equal amounts of water at about 
10° above the temperature of the 
room. Read the thermometers 
again at intervals of a minute. 
Tabulate the results, and state 
what you have learned, as regards 
the effect of surface, color, etc., 
when 

(a) radiant heat strikes the surface; 

(b) the body radiates heat. 

State in your note-book three common examples of the 
application of these facts. 

EXERCISE 13. 

SOLUTION. 

EXPERIMENT. 

Apparatus.— Five test-tubes; water, and means of warming it; 
measuring-cylinder; scales and weights (if solids are not ready 
weighed); powdered and lump sugar; burner; sand; iodine; copper 
sulphate; alcohol. 

Object. — To observe the conditions affecting solution. 




Fig. 81. 

on absorption of heat 



152 HEAT. 

Manipulation. — Part I. Take two test-tubes, place in 
each 0.5 gram of powdered sugar; to one add 5 and to 
the other 10 cu. cm. of warm water. Cork the tubes, and 
shake gently until all the sugar is dissolved ; then add a 
second 0.5 gram to each, and so proceed as long as the so- 
lution goes on. Set the tubes aside. Can any amount of 
sugar be dissolved in a given amount of water ? Does the 
volume of water used have any effect ? 

Part II. Place a piece of lump-sugar weighing about 
0.5 gram in one tube, and an equal weight of powdered 
sugar in another. Put about 5 cu. cm. of warm water in 
each, shake gently, and observe the time required to dis- 
solve. Does the condition of the body make any differ- 
ence ? 

Part III. Warm one of the tubes containing the solu- 
tions formed in Part I. Then add another 0.5 gram sugar, 
and heat. Does the temperature of the water have any 
effect on its power to dissolve ? 

Part IV. Take five test-tubes, place in them about 
equal amounts (0.25 gram) of sugar, sand, iodine, copper 
sulphate, and alcohol. Add to each 5 cu. cm. of water. 
Are all bodies equally soluble? Can one liquid dissolve in 
another ? 

Part V. Repeat the experiment with alcohol. Does the 
nature of the liquid make any difference ? 

Part VI. Place about 40 cu. cm. warm water in a meas- 
uring-cylinder; read the volume; now put into the water 
0.5 gram of powdered sugar, and again read the vol- 
ume. When the sugar has dissolved, read the volume 
again. What effect on the volume of the liquid is pro- 
duced by dissolving a liquid in it ? 

Tabulate all the conditions that you have found affected 
the solution. 



DYNAMICS. 



EXERCISE 1. 



ACTION OF A FORCE UPON A BODY. 

Preliminary. — In the following exercise we wish to 
study the behavior of a body when a force acts upon it. 
The force must be applied to a 
body that is free to move, or we 
cannot be sure that anything ob- 
served is due to the action of the 
force alone. If the body is sus- 
pended, the suspending wire takes 
its weight, and there is nothing to 
prevent its responding freely to 
forces applied horizontally. A 
string may be attached to the body, 
and pulled in various directions in 
a horizontal plane and with differ- 
ent degrees of force. The degree 

of force may be approximately, but not accurately, meas- 
ured by attaching a spring-balance. 



-^ 



EXPERIMENT 1. 

Apparatus.— Heavy body suspended by a wire ; piece of cotton 
string ; two spring-balances for Experiments 2 and 3. 

Object. — To see (1) what happens when a force acts on 
a body, and (2) the effect of the direction of the action. 

Manipulation. — Arranging the apparatus as shown 
in Fig. 82, pull the string from various points of com- 
pass, always at the height of the ball and parallel with the 

153 



154 



DYNAMICS. 



table. Make five trials, and record the results in a table 
arranged as follows: 

TABLE I. 



Direction 
of Pull. 


Action of Body. 







Indicate the direction of the pull by inserting N. for 
north ; W. for west ; N.E. for north-east; etc. 

EXPERIMENT 2. 

Object. — To see the effect produced by the magnitude 
of the force. 

Manipulation". — Attach a spring-balance to the string. 
Pull suddenly on the balance, trying to vary the amount 
of the pull without altering the time during which it is 
applied. A sudden "yank" is best, only not hard 
enough to break the string. Observe approximately the 
amount of the body's motion and the strength of the pull 
as shown by the reading of the balance-index. Only gen- 
eral results are expected. Make four trials, and record the 
results as follows : 



Force. 


Motion. 


Direction. 









In columns 1 and 2 insert the words, "more," "less," or 
"same," as the case maybe. In the third column place 
the initials of the points of compass, as before. 



ACTION OF A FORCE UPON A BODY. 



155 



Questions. — What is the inference in regard to the 
magnitude of the force ? Does the direction in which the 
force acts make any difference in this respect ? Make 
several trials in each direction, say three, making twelve 
trials in all. By studying the data obtained in both these 
experiments make a summary of what is indicated, as re- 
gards the action of a force on a body, in relation to (1) 
motion of the body, (2) direction of the motion as com- 
pared to the direction of the force, (3) amount of the 
motion as compared to the amount of the force. [This last 
in general terms only. ] 

EXPERIMENT 3. 

Object. — To observe the effects of equal and unequal 
forces acting in opposite directions. 

Manipulation. — Attach two spring-balances by springs 
to the weight and pull in opposite directions. Observe 
the motion of the body when the forces are equal. By 
suddenly pulling stronger on one balance, render them un- 
equal, and observe the results. Try several times, apply- 
ing the two forces in various directions, but always opposite 
to each other and parallel to the table. Mark one force + 
and one — and record, in a table, as follows: 



+ Force. 


— Force. 


Result on Body. 









Under each force place its value, obtained by reading 
the balance, and in the third column insert the words, 
" moved" or " no motion," as the case may be. In case 
the body moved in the direction of the -f- force, place the 



156 DYNAMICS. 

-j- sign before the word "moved"; if in the opposite direc- 
tion, the — sign. 

Questions. — 1. Under what conditions does the body 
move ? Under what conditions does it remain at rest ? 2. 
Does the fact that a body is acted on by forces necessarily 
mean that the body will move ? When a body is acted on 
by forces and the opposite forces are equal, it is said to be 
in equilibrium. Place in the note-books two cases of 
equilibrium that you know of, and explain in each case 
how the equilibrium is obtained. 

EXERCISE 2. 

THE FORCE OF FRICTION. 

Preliminary. — When two surfaces are rubbed together 
some force is exerted. This fact is said to be due to fric- 
tion of the surfaces, and the force with which the surfaces 
resist being rubbed is said to be due to the force of friction. 
In the following exercise we wish to study the conditions 
which affect the magnitude of this force. We must meas- 
ure the force under various conditions. Since the force 
required to keep a body moving over a level surface is 
equal to the force of friction acting upon it, if we ascertain 
the magnitude of one force, we know that of the other. 
By turning the block used in the experiments edgeways or 
flat, we can vary the extent of surface rubbed ; and by lay- 
ing one or two blocks on the first, Ave can double or treble 
the weight without altering the extent of surface. 

EXPERIMENT. 

Apparat us.— Board; blocks of wood; 8-oz. balance or rubber-strip; 
string. 

Object. — To study the conditions affecting the magni- 
tude of the force of friction. 

Manipulation.— Lay the block of wood on its smooth, 



THE FORCE OF FRICTION. 157 

flat side, and draw it along the board at a uniform rate of 
speed. Two students should work together on this experi- 
ment. One student, holding the balance horizontally on 
the palm of one hand, and grasping its ring with the other 
hand, should devote his whole attention to reading the bal- 
ance as his hands slide along the board, with a view to de- 
termining the average position of the pointer. The other 
student should see that the motion is uniform and the 
pull parallel. Eepeat several times, recording the force 
observed each time. Eepeat with the block turned on 
edge. Lay the block flat and place a second one on it. 
Measure the force again. Try again with two blocks laid 
on the first. Repeat the first part with the rough side of 
the block down. Tabulate results as follows: 



Position of Block. 


Force. 


Av. Force. 


No. of Blocks. Trial. 













Questions. — 1. What effect has the extent of surface 
on the force of friction ? 2. What effect has the weight ? 
3. What effect has the character of the surface ? 4. 
Weigh one block and calculate the coefficient of friction 
for all the weights, taking two blocks as twice the weight 
of one block, etc. 

Measurement of Forces. — If forces are to be compared as 
to strength, we must have a unit of force, just as we had units 
of length, volume, etc. We need for this unit a force that 
can be readily obtained, and easily used for purposes of 
comparison. The force selected is gravitation, as shown 
in the pull of the earth on bodies upon its surface. This 
pull has been found to be always the same for the same 
body at the same place, but in order to get a definite pull 



158 DYNAMICS. 

we must also specify the quantity of matter to be pulled. 
The unit of force is taken as the pull of the earth on a unit 
weight — say a pound weight or a gram weight; thus a force 
of one pound would be a push or pull equal to the pull of 
the earth on a pound weight. In order to pull with a 
force of one pound, you would have to exert your muscles 
as much as in holding a pound weight. In the same way, 
a force of one gram would be a force equal to the pull of 
the earth on a gram weight. 

Problems. — Explain what is meant by: 1. A force of 6 
lbs.? 2. A force of 1 ounce? 3. A force of 10 grams? 
4. A force of 1 ton? 5. A force of 6 kilograms? A 
pound weight weighs 453 grams. A force of 2 lbs. would 
be the force of how many grams ? 

There are two ways of measuring forces — by weights and 
by a spring-balance. In the first way, the weights are 
made to pull against the force to be measured, and a suf- 
ficient number of weights are used to just balance the 
force. The sum of the weights shows the value of the 
force. In the second way, the force to be measured is 
made to stretch the spring of the balance, and the value of 
the force is given by the index. A spring-balance when 
used for measuring force is sometimes called a Dynamom- 
eter. 

Graphical Representation of Forces. — To represent a 
force whose magnitude, direction, and point of application 
are known, we proceed as follows: 

1. Make a point for the point of application. 

2. To that point rule a straight line whose direction is 
the direction of the force. 

3. Assuming some particular length to represent a unit 
of force, with compasses or scale lay off this length along 
the line of direction as many times as there are units of 
force. 

For example, suppose we have to represent a force of 6 



THE FORGE OF FRICTION. 



159 



lbs. magnitude acting in an upward direction on the line 
ad, Fig. 83. Mark the point of ap- a 
plication anywhere on the line, say 
at c. To c draw a straight line cd. 
Starting at c, with a scale of 1 cm. to 
1 lb., lay off along cd a distance of 
6 cm. Suppose, again, we wish to 
represent another force of 3 lbs. act- 
ing at e. Draw to e a line eg, and 
from e lay off on it 3 cm. The di- 
rection of a force is sometimes rep- 
resented by an arrow. The fact 
that forces are acting in opposite 
directions is also indicated by giv- 
ing one the + sign and the other the FlG - 83 - 

— sign. Commonly, -|- is used for the upward direction 
and — for the downward, -\- toward the right and — to- 
ward the left, but since the general rule is to mark one 
force -f and all forces whose general direction is opposite 
— , the direction -|- represents should be stated in each 
diagram. Forces are added by laying off on the line rep- 
resenting the forces of one sign a line representing the 
forces of opposite sign. Thus, to find by construction the 
sum of -j- 6 and — 4, lay off on the line |6 a distance 
equal to — 4. The part of the length not used up by the 

— length is the required sum, -|- 2 in this case. 

A problem can be worked out, as most convenient, by 
geometry, using lines as above, or by algebra, using num- 
bers and signs. In the latter method the sign prefixed to 
the magnitude of a force indicates its direction relative to 
the other forces. These magnitudes are added and sub- 
tracted as other algebraic quantities. Thus the sum of 
two faces, one + 6 and — 4 is a force of -f- 2. 



160 DYNAMICS. 

EXERCISE 3. 

COMPOSITION OF FORCES. 

Preliminary. — A force that in its action on a body is 
equal to the combined effects of several forces is called the 
resultant of those forces. For example, a single force 
which will produce the same effect on a horse-car as the 
force exerted by the two horses would be the resultant of 
the forces exerted by the horses. The process of finding 
the resultant of several forces is called the composition of 
forces. The reverse process, finding several forces whose 
combined effect on a body is equal to that of a given force, 
is called resolving that force, and the equivalent forces 
found are called its components. 

We can apply more than one force to a body at one 
point in two ways. 

(a) We can apply the forces in one straight line, in the 
same direction or in opposite directions, as a number of 
engines drawing a train, or two men pulling against each 
other on a rope. In the first case each force adds its effect 
to that of the others; in the second case, the lesser force 
diminishes the effect of the greater. The resultant of the 
forces in each case is their algebraic sum. For example, a 
wagon is pulled by three horses tandem, each exerting a 
force of 1000 lbs. ; the same effect on the wagon would be 
caused by one horse exerting a force of 3000 lbs. Or, again, 
a body is acted upon by two opposite forces, +8 — 3, in 
strength; the same effect would be produced on the body 
by a single force -j- 5 in strength. 

(b) We can apply the forces at an angle to each other. 
Suppose two forces act on the same point, one pulling it 
east and one pulling it north. Can a single force be found 



COMPOSITION OF FORCES. 



161 



that, when applied alone to the point, will produce the same 
effect as the two forces ? To answer this question we must 
let two forces act on a body at an angle, and see if we can sub- 
stitute for them one force that will produce the same effect. 
If we can do so, the substituted force will be the resultant. 
Two balances, A and B, Fig. 84, are joined by a cord. 
On this cord slides another whose ends are attached to two 




other balances, C and D. A and B are fastened to the 
table, and by pulling on C two forces will act on the point 
a at an angle AaB. The balance C will hold this point 
against the combined action of A and B, and this com- 
bined action will pull the index of G down to a certain 
point, and a will take a certain position which can be 
marked. Now if we release A and B, and by pulling on D, 
as in Fig. 85, can bring a to the same point, we shall have 
substituted the pull of a single balance for the combined 
pulls of the two balances, A and B. It will be also desir- 
able to find out whether a single force acting on a point can 
be resolved into two components acting at an angle on the 
same point. We can do this by pulling on a with a certain 
force registered on C, and then trying to substitute angu- 
lar pulls by A and B that will bring a to the same point. 



162 



DYNAMICS. 



EXPERIMENT 1. 

Apparatus.— Four 24-lb. balances; fish-line; scale; dividers; nails'; 
wooden block. 

Object. — When two forces act at an angle on the same 
point, to find one force whose effect on the point is the 
same as the combined effects of the other two. 

Manipulation. — Arrange apparatus as in Fig. 84, A and 
B being fastened to the table. Pull on C in any direction 
until it and A and B read over five pounds. In a general 
way, the stronger the pulls the better, only care must be 
used not to break the strings. Either hold the balance 
steady; or, better, secure it by a nail passing through the 
ring and driven into the table. Read the balances, and 
mark the position of the point a on the table. Pull on D 
with a force of a few pounds, and, still keeping a strain on 
D, gently release the balances A and B. Then by pulling 
on D, find the direction and magnitude of a force that will 
bring a to exactly the same point as when acted on by A 
and B. If you succeed in doing this, you will have one 
force producing the same effect on a as the combined forces 
A and B. Make several trials, and record the results as 
follows : 



Force A. 


Force B. 


Force C. 


Force D. 











Questions. — 1. How do C and D compare in magni- 
tude? 2. How do they compare in direction? 3. How 
does the general direction of D compare with that of A and 
B? 4. How does the magnitude of D compare with those 
of A and of B? 5. How does the magnitude of D com- 
pare with the sum of the magnitudes of A and Of 



COMPOSITION OF FORCES. 



163 



EXPERIMENT 2. 

Apparatus.— Four spring-balances; stout string; nails; etc. 

Object. — To find two forces that, if applied to one point 
at an angle to each other, will produce the same effect as a 
single given force applied to the same point. 

Manipulation. — Arrange apparatus as in Fig. 85, A 
and B being loose and G being fastened to the table. Pull 
on D with any desired force in any direction, and note the 
readings of G and D and the position of a. Substitute for 




D, A and B pulled at an angle. See if their combined 
effect can be made to bring a to the point where it was 
when and D alone acted on it. Make several trials with 
a view to finding out whether more than one combination 
of A and B can take the place of D. Eecord in each case 
the balance readings, and the angles made by A and B as 
estimated by the eye. 

Questions. — 1. Can two forces produce the same effect 
as one ? 2. Can they be substituted for one ? 3. How 
do their magnitudes compare with that of the one for 
which they are substituted ? 4. Can more than one set of 
forces be substituted for the given force ? 

Parallelogram and Forces. — The next thing is to find a 
way to express graphically the relation of the resultant 
and its components. The readings of A and B in the 



164 DYNAMICS. 

apparatus represented in Fig. 84 will give the magnitudes, 
and the strings the directions of the components. Taking 
these directly from the apparatus, we can construct a 
parallelogram whose two adjacent sides represent the two 
components. Since, as we have just seen, the third force, 
C, is equal and opposite to the resultant, we can include 
the resultant in the parallelogram by taking the reading 
of C for its magnitude and making its direction exactly 
opposite to that of the string Ca. In the diagram we can 
look for any geometrical relation that may exist between 
component and resultant forces. 

EXPERIMENT 3. 

Apparatus.— Same as in Exp. 2, and a thick block of wood to be 
used as a ruler. 

Object. — When two forces act at an angle on the same 
point, to exjiress graphically the relation between them 
and their resultant. 

Manipulation. — Proceed as in Exp. 2. When all three 
balances are pulling on the point a, place the note-book 
under the strings so that the knot comes about in the 
centre of the page, Fig. 84. Bring the block of wood 
gently up to one of the strings so as to just touch it at all 
points, and, using it as a ruler, draw a line a few inches 
long. This line should represent exactly the direction of 
the string. Great care must be used not to move the 
string and not to let the block of wood touch the knots at 
either end. The harder the balances are pulling, the less 
the string is likely to be deflected. Do the same with the 
other two strings, using great care that the note-book does 
not change its position during the operation. Read each 
balance, and put its reading at the outer end of the corre- 
sponding line. Remove the note-book, and by means of a 
ruler prolong the lines until they meet at a point as indi- 
cated by the dotted lines in Fig. 86. This is the point, a, 



COMPOSITION OF FORGES. 165 

which was directly under the knot. You have now the 
magnitude, direction, and point of application of the three 
forces.* Starting from the point a, lay off on the lines 




Fig. 86. 

9 and 8 the magnitudes corresponding, representing 1 lb. 
by the largest unit of length the note-book page permits. 
Construct a parallelogram, of which the point a forms one 
angle and the lines representing the two forces 9 and 8 
form the sides adjacent. The junction of the opposite 
sides is found by prolonging the line representing the 
third force, 12, as a diagonal through this parallelogram, 
and from a laying off on it a distance equal to that force. 
Make as many trials as time allows, using various forces. 
From the study of the diagrams so obtained make a rule 
for finding, by means of a diagram. 

1. The resultant of two forces whose magnitudes and 
directions are known. 

2. The components of a given force. 

* Before laying off the forces, the balance-readings should be 
corrected for position error and zero error, if these errors are of 
magnitude. Usually, however, as they tend to counteract each 
other, the total error is so slight that it may be neglected. The 
record in the note-books should state whether or not corrected 
readings are used. 




166 DYNAMICS. 

EXERCISE 4. 

PARALLEL FORCES. 

Preliminary. — So far as we have considered cases where 
the forces had the same point of application; but there is 
another case. Suppose the body ab, Fig. 87, to be acted 

on by two parallel forces, x and 
>* y. A good illustration of this is 

where a carriage is pulled by a 
>y span of horses. In this case it 
fig. 87. is evident that the two forces 

have different points of application, and that the resultant 
has a still different point. Forces applied in this way are 
called parallel forces. To investigate the case of parallel 
forces the apparatus shown in Fig. 88 is used. By pulling 
down on the balances B and C, parallel forces act on the 
meter-stick, and the combined pull of the two is taken by 
balance A. The readings of B and (7 give the magnitudes 
of the components, and the reading of A the magnitude 
of a force which is equal and opposite to the resultant (as 
in Ex. 3), and whose point of application is the same as 
that of the resultant. With these data we can investigate 
the relations, as regards magnitude, point of application, 
etc., of parallel components and resultant. 

EXPERIMENT 1. 

Apparat us.— Three 24-lb. balances; meter-stick; fish-line; means of 
suspending meter-stick (the whole arranged as in Fig. 90). 

Object. — When two parallel forces act on a rigid body, 
to determine (1) the relation of the resultant to the com- 
ponents in magnitude and direction; (2) the position of 
the point of application of the resultant with reference to 
those of the components; (3) under what conditions equi- 
librium may be obtained ; and (4) under what conditions 
the body tends to rotate. 



PARALLEL FORCES. 



167 



Manipulation. — The readings of B and G, Fig. 88, 
when forces are applied will not represent the true forces, 
because the balances themselves weigh something, and alone 



1=777777 




I il 1 1 1 1 'I i 1 1 1 ? 1 1 1 > I 




exert a slight downward pull. To correct for this error, 
detach the apparatus from the balance A, slip the loops of 
string off from the meter-stick, and weigh balances B and 
on A. Take half the weight so obtained as the weight 
of one balance.* Again, since balance A has to support the 
weight of the meter-stick in addition to the forces used, 
the weight of the meter-stick must be found. Eemove 
balances B and G from A, suspend the meter-stick alone, 
and record the reading of A. Since this reading also gives 
A's increased reading due to the zero, error, we have the 
total amount to be subtracted from each subsequent read- 
ing in order to get the true force exerted on A by the com- 
bined pulls of B and G. When ready for work, the table 
of errors should stand something like this: 

Correction for weight, B G. . . .A . . . . 

to zero, B....G 

Eecord on which side of the pointer the readings were 
taken. 

Slide the loops of the strings from B and G to such 



* These weighings could be still better performed with a 64- oz. 
balance. 



168 



DYNAMICS. 



points on the stick that the distance of each loop from the 
centre is over 10 cm. Pull down steadily on the two lower 
balances, being careful to pull vertically, until each balance 
reads more than five lbs. Read the three balances, and note 
the direction of balance A. Place the loops at different 
points on the stick, and try again. Try a case where the 
distance on one side is twice that on the other. Try a case 
where the distances are both alike. Try other cases, mak- 
ing six in all. Great care must be used in reading the 
balances as accurately as possible, and always from the 
side of the pointer used in getting the readings for errors. 
Tabulate tjie results as follows : 



Read. A. 


Read. B, 


Dist, B. 


Read. C. 


Dist. C. 


Direc. A. 


Trial. 

















While you have equilibrium, increase the pull of one 
balance. Note what happens. Decrease, and note again. 

Calculation". — The balance-readings have three errors 
for which corrections must be made: (1) Owing to use, the 
balances all read high; (2) A reads high because of the 
weight of the apparatus; (3) The readings of B and C show 
the forces applied less the weight of the balances them- 
selves and their zero-errors. Correct A by subtracting total 
weight-error. Correct B and C for zero- error, and add 
their-weight. Record the results as follows, giving cor- 
rected readings: 

TABLE II. 



Read. A. 


Read. B. 


Read. C. 


Dist. B. 


Dist. C. 


CxDc 


BxDb 

















The values obtained by multiplying the magnitudes of 
parallel forces by their " leverage," that is, the distance of 



THE INCLINED PLANE. 169 

the point of application of each force from the same point 
of reference, as C x Cd, Fig. 88, are called the moments 
of the forces. 

Questions. — 1. Can yon see any relation between A, B, 
and C as regards (a) direction; (b) magnitude? 2. Is 
anything noticeable on comparing the moments of B and 
for each case ? 3. Can you make out any relation between 
B and Db that also exists between C and Dc ? 4. When 
the stick is at rest, how do the moments of B and C com- 
pare? 5. When the moment of one force was made larger 
than the other, by suddenly pulling down on one balance, 
what happened ? 6. Can you name a case in which the 
principle of this experiment is used ? 

EXERCISE 5. 

THE INCLINED PLANE. 

Preliminary. — We know that machines enable us to 
make a small force overcome a greater one, but do they 
save work ? When a force is overcome by the aid of a ma- 
chine, is any less work done than when the force is over- 
come directly ? For example, if a weight is lifted directly 
10 ft., or lifted the same distance by a machine, is the 
work done in the former case any more than that done in 
the latter ? To answer this question, we may raise a known 
weight a known vertical distance by means of a machine, — 
say an inclined plane, — and compare the work done in this 
case with that done in lifting the body vertically the same 
distance. For this purpose the apparatus illustrated in 
Fig. 89 may be used. The board B forms the inclined 
plane, and may be set at any angle by adjusting the rod R 
of the support S. The weight to be raised is the loaded 
carriage C, and the force required to pull it up the plane 
may be obtained from the reading of the balance B. We 
can get the work done in raising the body vertically by 
multiplying the total weight of the body by the distance it 



170 



DYNAMICS. 



is raised (say ab in the figure), and the work done in rais- 
ing it by the plane by multiplying the force required to pull 




Fig. 89. 

the body up the plane by the distance that it must travel 
on the plane, cb in the figure, to reach the required height. 

EXPERIMENT. 

Apparatus.— Board of Exercise 2; support; weighted carriage; 
24 -lb. balance; cross-stick and cord; meter-stick; T-square or 
plumb-line. 

Object. — 1. To study the laws of the inclined plane. 2. 
To see if a machine, taking the inclined plane as an exam- 
ple, saves work. 

Manipulation. — Get the weight of the carriage and 
load together.* In case no suitable scales can be had, the 
weight may be found with sufficient accuracy by means of 
the spring-balance. Adjust the support so that the board 
B is inclined at an angle of about 30 degrees. Hook the 
balance into the loop at the end of the cord connected with 
the carriage. Let one student hold the balance firmly in 
both hands, and draw the carriage up the plane at a uni- 
form rate of speed. The back of one hand should rest on 
the board upon which it slides, and his entire attention 
should be devoted to holding the balance firmly, and pull- 
ing the carriage at a uniform rate. He should pull exactly 
parallel to the plane, and hold the balance so that it will 
not bind, keeping his eyes away from, the balance altogether. 

* This weight may be determined once for all, and marked upon 
the carriage. 



THE INCLINED PLANE. 



Ill 



Meantime let the second student keep his eye directly over 
the balance and take as many readings as possible. Owing 
to little inequalities in the board, etc., these readings will 
vary slightly, and the average position of the index must be 
determined as accurately as possible. A number of trials 
should be made, the students alternating in reading the 
balance, etc., and different parts of the board being used. 
The average of these trials, after the following corrections 
have been made, will give very closely the force required to 
pull the carriage and load up the plane. 

The force used to pull the body up the plane is not the 
true force required, because a portion of it is expended in 
overcoming the friction of the carriage-wheels, etc. To 
correct for this slight excess in the reading of the balance, 
let the body slide down the plane at the same rate of speed 
at which it was pulled up, reading the balance as before. 
When the necessary correction for the zero error of the 
balance has been made, the average of the two readings 
will be very nearly the true force required. 

Carefully measure the distance the body must travel on 
the board for a vertical rise of one foot, db in the figure, 
or any vertical distance suitable to the apparatus. If a 
" T-square " can be obtained, the vertical rise taken may 
be marked off upon one side of it, starting from the outer 
edge of the cross-piece. The T-square is then placed ver- 
tically upon the table resting against the board, as shown 



in Fig. 90, and slid along until 
the mark indicating the vertical 
distance coincides with the lower 
edge of the board. The distance 
from this point to the lower cor- 
ner of the board is the length of 
the plane to be measured. If no 
T-square is available, a plumb-line 
of the required length may be 



dropped from the lower edge of the board and slid down 




172 



DYNAMICS. 



until it just touches the table. The method with the T- 
square is the best. 

Change the angle of the board and repeat the experi- 
ment. Tabulate results as follows: 

TABLE I. 



Approx. Angle 
of Board. 


Up-force. 


Down-force. 


Vertical Rise 
of Body. 


Distance on 
Plane. 













Calculation. — From the results of Table I, calculate 
and arrange the data under the following headings, where 
W= the weight of the body, F = the true force required 
to pull the body up the plane, Dv = the distance the body 
was raised vertically, and Dp = the distance the body 
moved on the plane for this vertical rise. 

TABLE II. 



w. 


F. 


Dv. 


Dp. 











Questions. — 1. What effect has the angle of the board 
on the force required to pull the body up the plane ? 
2. What effect has the angle of the board on the distance 
the body must travel on the plane for a given vertical 
rise? 3. Can you make out any relation between IF' and F 
that also exists between Dv and Dp ? 4. Calculate for 
each case the work done in raising the body the given ver- 
tical distance, say 1 ft., and the work done in raising it the 
same distance by means of the plane.* 5. Can any rela- 

* In the first case, this equals 

WX Dv, 
and in the other 

^X Dp. 
These may be calculated in any units of work, but the same units 
must be used in each case. Compare the values so obtained. 



THE WEDGE AND THE SCREW. 173 

tion be made out between the work done in raising a body 
a certain distance vertically and the work done in raising 
it the same distance by the plane ? Does this hold for 
more than one angle of the plane ? 6. Does the machine 
save work ? (i.e., is less work done when the plane is used 
than when the body is lifted vertically?) 7. How does the 
machine help you ? 

EXERCISE Q, 

THE WEDGE AXD THE SCREW. 

Preliminary. — In the following exercise it is desired to 
discover whether the facts just observed also hold when 
the force used to draw the body up the plane is applied 
parallel to its base, as in the wedge and the screw, instead 
of to its length, as in the inclined plane. For this purpose 
the same apparatus may be used, the force being applied . 
by pulling the balance parallel to the table instead of to 
the board. 

EXPERIMENT. 

Object. — 1. To study the laws of the wedge and screw. 
2. To see if the inferences drawn for the inclined plane 
will hold for the wedge and screw. 

Manipulation". — Attached to the front of the carriage, 
C, Fig. 89, is a stick long enough to extend beyond the 
support at both sides. A second stick of the same length 
is connected with the first by cords, as shown by dotted 
lines, and the balance is attached to the centre of the 
second stick. As the connecting cords pass outside of the 
support, the body can be pulled up and down the plane 
without difficulty, by a force parallel to the table. Let one 
student hold the balance in both hands, face up, and pull 
the carriage up the plane, keeping the strings parallel to 
the table by raising his hands as the body rises on the 
plane. A second student should stand a short distance 
away, where he can see if the pull is actually parallel to the 



174 



DYNAMICS. 




table. The students should alternate in reading the bal- 
ance. 

Make the observations, records and corrections, and 
answer the questions, as in Ex. 5. 

EXERCISE 7. 

LAWS OF THE PENDULUM. 

Preliminary. — The apparatus used in this exercise is 
shown in Fig. 91. Near the 
edge of the support S (which 
may be the edge of a table or 
shelf) is screwed a spool S'. The 
screw is "set up" until the spool 
turns with considerable friction. 
A string is wound around the 
spool and is held in place by pass- 
ing through the slot of a screw, 
E, inserted horizontally in the 
edge of the support. The lower 
end of the string passes through 
a hole in a metallic ball B which 
forms the pendulum-bob. The 
length of the pendulum may be 
varied by turning the spool so as 
to wind or unwind the string. 
Small adjustments are best made 
by gently turning the spool. 

EXPERIMENT. 

Apparatus.— Two iron balls of different sizes, or iron and wooden 
balls; apparatus for suspension (screw, spool, fish-line); callipers or 
rectangular blocks to get diameters; meter-stick; time-piece. 

Object. — To determine the effect on the number of vi- 
brations of a pendulum, of (1) length of arc, (2) length of 
pendulum, (3) weight of bob. 

Manipulation. — Part 1. Length of arc. Make the 
length of the pendulum about 50 cm. Count the number 



LAWS OF THE PENDULUM. 175 

of vibrations it makes in two minutes when swinging 
through an arc of not over 30 cm. Increase the arc to, 
say, 60 cm., the length of the swing being estimated by the 
eye. Determine as before the number of vibrations in two 
minutes. Compare the number of vibrations a minute in 
each case and draw your inference. Record the results as 
follows : 



Arc. 


No. Vibrations in 2 min. 


No. Vibrations per min. 


Long 
Short 







From the observation of the data, infer the effect of 
length of arc. 

Part 2. Length of pendulum. Observe the general ef- 
fect of changing the length of the pendulum. Eecord 
your observations and inference in general terms. 

To make the quantitative determination, we must com- 
pare the number of vibrations in equal times of pendulums 
of different measured lengths. The length of the pendu- 
lum is the distance from its centre of gravity to its point 
of support. The string having practically no weight, the 
centre of gravity of the pendulum corresponds with that 
of the ball, and is in the centre of the ball. To find the 
length of the pendulum, therefore, we must measure the 
distance along the string from the lower edge of the screw 
to the top of the ball, and add to it half the diameter of 
the ball. Place the lower end of the meter-stick on top of 
the ball, and bring its graduated edge up to the string. 
Measure the distance to the edge of the screw three times, 
reading to millimeters. The average of these three read- 
ings will probably be nearly correct. Get the diameter of 
the ball, where the hole is, by placing it between the jaws 



176 



DYNAMICS. 



of the callipers and then applying the callipers to the scale. 
Repeat three times and average.* The length of the string 
plus half the diameter of the ball is the length of the 
pendulum. 

Set the pendulum swinging through an arc of about 
2 ft. Measure the number of vibrations in 1, 2, and 3 
minutes. Eeduce the length of the pendulum about half, 
measure exactly, and repeat the counting. Record results 
as follows : 



Length of 
String. 


Av. L. of 

String. 


Diam. of 
Ball. 


Av. D. 


® . True 
2 'Length. 


No.Vib. 


Time. 


Av. No. 
Vib. 










1 

1 









Part III. Weight of the bob. Substitute for the ball 
on the pendulum a larger ball. Carefully determine the 
diameter of the second ball, as before. Make the length of 
the string such that the length of the pendulum is the 
same as before, i.e., the length of the string plus the radius 
of the ball equals one of the lengths used in Part II. De- 
termine the number of vibrations in 1, 2, and 3 minutes as 
before. Record as in Part II. Compare the average num- 
ber of vibrations per minute with that of similar length in 
Part II. 

Calculation. — Divide the smaller length in Part II by 
the larger. Divide the smaller number of vibrations by the 
larger. Compare the ratios so obtained. If they do not 
agree, try squaring or cubing one of the ratios, and find the 
values approximating most closely. Infer the law, and ex- 
press it as a formula. 



* Or use the method given in notes on Mensuration. 



ACTION AND REACTION. 



177 



EXERCISE 8. 

ACTION AND EE ACTION. 

Preliminary. — In this exercise we experiment with two 
bodies by giving them various amounts of energy and 
allowing them to collide. The special point of the experi- 
ment is to compare (1) the energy possessed by each body 
before and after the collision, (2) the energy lost by one 
with that gained by the other, and (3) the results of trying 
elastic and non-elastic bodies. The apparatus used is shown 




in Fig. 92. Two ivory balls, A and B, are so suspended 
that they can swing in one plane only, and will collide at 
the lowest point of their arc. They may be drawn aside 
any desired distance and held there by the electro-magnets 
CO, and released by breaking the circuit. The distances 



178 DYNAMICS. 

they are drawn aside may be read on the scale by aid of the 
cards bb. The momentum in each case is taken as the 
product of the weight of the ball multiplied by the distance 
it moved. 

EXPERIMENT I. 

Apparatus. — Two ivory balls; No. 30 wire; electro-magnets; board; 
two meter-sticks; electric current; circuit-breaker; tacks; made into 
apparatus as shown; scales and weights (if balls are not of known 
weight). 

Object. — To compare (1) the algebraic sums of the ener- 
gies possessed by two "bodies before and after collision, (2) 
the results of trying elastic and non-elastic bodies, (3) the 
direction of the action and reaction, (4) the energy lost by 
one with that gained by the other. 

Manipulation. — A little adjustment of the magnets as 
regards their position in the plane of oscillation will enable 
the student to release the balls so that they will strike 
squarely upon each other. By means of the index-cards cc, 
determine on the meter-stick the position of the balls when 
at rest. One ball being at rest, place the magnet so as to hold 
the other ball about 10 or 15 cm. aside. Bead the position 
of this ball by the index-card b. Break the circuit, thus 
allowing one ball to strike the other, and notice the dis- 
tance traversed by each ball after collision. Place an index- 
card at each of these points, and repeat the experiment. 
Sighting across each index, note the exact position reached 
by the centre of the corresponding ball, and place the index 
at this point. Try again until each index marks the exact 
position reached by centre of the corresponding ball after 
collision. As the magnet remains in the same place all the 
time, the distance traversed by the ball before collision is 
always the same, and need not be measured again. Follow- 
ing this method, try the following cases, calling the small 
ball B, and the large ball A : 

Case 1. A in motion, B at rest. Try two cases, and re- 
peat with B in motion and A at rest. 



AGT10N AND REACTION. 



179 



Case 2. Kelease both balls at once. Try covering one 
ball with a thin layer of putty. The weights of the balls 
should be determined in each case. 

Compare the momenta before and after collision in each 
case. Distinguish between the behavior of elastic and in- 
elastic substances under these circumstances. In calculat- 
ing the momenta, call the movement towards the right 
hand -}-, towards the left hand — . Tabulate results as 
follows : 

Weight of A ... . Weight of B. . . . 





w" 


* 


^ 


•s 




R? 


£ 


^ 


£. 


05 




u 




£ 


03 


•^ 


'So 


&. 


"g^ 


>> 




o3 








■C 




JS ° 








"3 


^ 


o3 © 


cq 


xq 


> » 

o3 0) 


8ft 


^ 


O Sh 


> O 

03" 


£ 


O 


OTS 


■^ O 


o 


Ot3 


-^ O 






^ 


-^ s 


6 




£% 


.2 -JO 






.22-° 


g^ 


iSStf 


§05 


.52 «8 


fc 


Ph 


Ph 


Q 


P^ 


Ph 


Q 


On 


Q 


Ph 


Q 

























From the above data calculate the momenta before and 
after collision in each case, being careful to keep the proper 
signs. Arrange results as follows : 

Case 1. Momentum of A before collision = 
" A after "■ = 

" B before " = 

" B after " = 

Algebraic sum = 

From these data answer the questions given in the object. 

SUBSTITUTE EXPERIMENT. 

Apparatus.— Two pint tin pails, suspended and adjusted as shown; 
heavy bodies to load pails; cotton string; candle; two meter-sticks; 
coarse scales. 

Object. — (1) To compare the values of action and re- 
action when two bodies are acted upon by the same force, 
and (2) to study the effect of varying the weight of the 
bodies. 



180 



DYNAMICS. 



Manipulation.— Set up the apparatus as shown in Fig. 
93. Call the pail with the spring A, and the other B. 
Detach B from the wires, and make it weigh 250 grams 
(cover on). Compress the spring and tie it with a string.* 



fci's 



' .....'...:. 



gHsL 



»£ji 



"-• , ' : 



In the same way make A weigh 500 grams. Attach both 
the pails to the wires, being sure that they hang vertically. 
Holding the eye directly above the outer edge of each pail 
in turn, read its position on the meter-stick underneath, 
and record. Now place a meter-stick under the edge of 
each pail, and burn the string. As the pails swing out 
keep a pencil directly under the outer edge of each one, 
and stop them at the extreme point of the swing. While 
the pails return, hold the pencils steady at these points, 
read their positions on the meter-sticks, and record. Re- 
peat three times; then make pail B 500 grm., and try again, 
say three times more. If possible, try again with 750 grm. 
Tabulate results as follows : 

* It is a good plan to bold the hand between the pails when they 
come together, so that they will not strike each other with a heavy 
blow. 



THE FORCE OF TENACITY. 
TABLE I. 



181 



Wt. A. 


Wt. B. 


Read. A 

at rest. 


Read. B 
at rest. 


Read. A 

at end of 

swing. 


Read. B 

at end of 
swing. 















From the data in Table I calculate the following table: 

TABLE II. 



Wt. A. 


Wt. B. 


Dist. A moved. 


Dist. B moved. 


Wt. A x 
Dist. A. 


Wt. B x 
Dist. B. 















Questions. — 1. Can any relation be made out between 
the weights of the pails and the distances that they moved ? 
2. What relations appear between the numbers in the last 
two columns in Table II? 3. Calling w and W the 
weights of the two pails, and d and D the distances moved, 
can the results be expressed as a formula? 4. Can any 
law be inferred for the relation of action and reaction re- 
garding (a) direction, (b) extent of motion ? 



EXERCISE 9. 

THE FORCE OF TENACITY. 
EXPERIMENT. 

Apparatus.— Wire of two sizes and two materials; 
screwed to table; 24-lb. spring-balance; meter-stick. 



ha If -spool 



Object. — To study the effect of length, cross-section, 
and material on the force of tenacity. 

Manipulation". — Part L Effect of Length. Pass one 
end of the wire twice around the half-spool with a 
"round turn," making it lie close to the spool all the way; 
then twist the end of the wire around its main part, as 



182 



DYNAMICS. 




indicated in Fig. 94. The spool is screwed to the table. 

Cut off the wire about 
one meter from the spool, 
and attach the end to the 
balance-hook, precisely 
jno,W4, as shown in Fig. 94. Ex- 

amine the wire to make sure that it is free from " kinks/' 
and measure its length. Then, holding the balance hori- 
zontally in the palm, move the hand along with its back 
on the table so as to produce a steady pull on the wire. 
Steadily increase the pull until the wire breaks, meantime 
watching the index of the balance all the time so as to 
know where it stands when the wire breaks. The first 
trial will tell about what part of the scale to watch in sub- 
sequent trials. Make four trials besides the first, and try 
to read to £ lb., especially in the third and fourth trials. 
Take a different length for each trial, and record the 
length of each piece. 

Part II. Effect of Cross-section. In the same manner 
determine the tenacity of the second size of wire, making 
four trials. 

Part III. Effect of Material. Determine in the same 
way the tenacity of the wires of different material, making 
four trials. 

Tabulate results as follows: 



No. Trial. 


Length of Wire. 


Cross-section. 


Bk.Wt. on Bal. 


Correct Bk.Wt. 











The values in the last column are the balance-readings 
corrected for zero and position errors. 

Questions. — 1. Can you make out any relation between 
length and tenacity ? 2. Between cross-section and tenac- 
ity ? 3. Has material any effect ? 4. What cross-section 



THE FORGE OF ELASTICITY. 



183 



of one wire would give the same tenacity as another wire 
of different cross-section and material ? 

EXERCISE 10. 

THE FORCE OF ELASTICITY. 

Preliminary. — A body whose shape has been changed by 
the action of a force is said to be distorted. A body which 
tends to take its former shape when distorted is said to be 
elastic. The force with which a distorted elastic body 
tends to resume its original shape is called the force of elas- 
ticity. A body which may be considerably distorted with 
very little force is said to be very elastic, or to have low 
elasticity. Eubber is an example of low elasticity. A body 
which gives considerable force of elasticity on small distor- 
tion is said to have high elasticity. Steel is an example of 
high elasticity. The following exercise 
investigates the effect of (1) degree of 
distortion, (2) cross - section, and (3) 
length on the magnitude of the force of 
elasticity in a solid. For this purpose 
the apparatus in Fig. 95 is used. The 
rubber strip S is fastened at its upper 
end, and may be stretched (distorted) by 
weights placed in the scale-pan E, which R A j 
is attached to its lower end. Since, after 
the strip has stretched and is at rest, the 
up pull due to the elasticity of the rub 
ber, and the down pull due to the weights 
must be equal, the weights measure the 
force of elasticity. The total amount of 
distortion is measured by reading the 
position of the point a on the meter-stick, 
by means of the reading-card 0. The 
distortion of two lengths, one twice the 
other, may be compared by reading first FlG - 95 - 

from the point a, and then from point b. The position of 




184 DYNAMICS. 

the card C may be changed by slipping off the rubber 
bands RR, and sliding it along the meter-stick. 

EXPERIMENT. 

Apparatus.— Apparatus for the experiment as shown ; weights 10 
to 200 g. ; screw-driver. 

Object. — (1) To see if any relation can be found between 
the amounts of distortion of an elastic body and the cor- 
responding magnitudes of the force of elasticity. (2) To 
observe the effect (a) of cross-section, (b) of length. 

Manipulation. — Part I. Adjust C so that the upper 
edge of the card touches the lower edge of the mark a on 
the rubber strip. Hold it there by hand or by the rubber 
bands, and read and record the position of the upper edge 
of the card on the meter-stick. Gently place 20 gr. on the 
scale-pan, and after the strip has come to rest, again adjust 
C, and read the position of a and record. Kepeat with 40 
gr. in the pan, and so proceed for ten readings in all (up to 
200 gr.). Record as follows: 



Weight used. 


Position of a. 


Distortion of S* 









Part II. Repeat Part I, reading from o, and record in 
the same way. 

Part III. Detach the strip used in Part II, and substi- 
tute the wide one. Repeat with this strip. When read 
from the mark upon it, this gives the same length and 
cross-section as the one in Parts I and II. 

Questions. — What effect have length and cross-section? 
2. Are all bodies equally elastic? (Answer from your gen- 

* The position of a for each weight minus that for no weight. 



BOYLE'S LAW. 



185 



eral knowledge.) 3. What conditions have you found to 
affect the magnitude of the force of elasticity ? Plot a cure 
from the data of Part I. 

EXERCISE 11. 

BOYLE'S LAW. 

Preliminary. — We know that when pressure is exerted 
on a confined volume of gas its volume becomes less, and 
that when the pressure is diminished the volume increases. 
In the following exercise we wish to see if we can find any 
relation between different pressures and the corresponding 
volumes.* 

The apparatus used is shown in Fig. 96. A glass tube, ab, 
is bent as shown. The short arm is closed at the top, the 
long arm open. The gas to be 
experimented upon is confined 
at b in the short arm by pour- 
ing mercury into the long arm. 
The pressures can be changed 
by using different depths of 
mercury, the volume of gas 
can be read on the scale d, and 
the depths of mercury on the 
scales d and e. The two cards 
ff help in reading the levels. 
As we know from the laws of 
liquid pressure, the depth, of 
mercury causing the pressure 
will be the difference in the 
heights of the two columns; 
and since the atmospheric I 
pressure is exerted on the top 
of the column in a, the total pressures will equal the 




* Suggest a method for such an experiment. 



186 DYNAMICS. 

height of mercury, causing the pressure plus the height 
of the barometer, whose reading must be known. Since 
changes of temperature affect the volume, the tempera- 
ture must be practically uniform during the exercise. 

EXPERIMENT. 

Apparatus.— As shown (tube; support; scales; reading-cards); 
about 500 gr. mercury (clean and dry); barometer; feather and rod 
to remove air. 

Object. — To discover some relation between the volume 
of a confined body of gas and the pressure exerted upon it. 

Manipulation. — Kead the barometer. (See the card 
of instructions tacked over the instrument, with instruc- 
tions for reading vernier, etc.) The barometer reads in 
inches; as the other readings will be in centimeters, con- 
vert the barometer-reading to centimeters by the following 
formula : 

Bar. -read, in inches _> , . 
w*7 = Bar. -read, m cm. 

Eead the thermometer. Place the glass funnel (be sure 
that it is clean and dry) in the open end of the long 
arm, and carefully pour in mercury until the bend is cov- 
ered and the mercury stands two or three cm. higher in the 
long arm than in the short arm. Tip to the left the appa- 
ratus as it stands in Fig. 96, and allow some air to escape 
from the short arm; place the apparatus upright again, 
note the levels, and, if necessary, repeat until the mercury 
stands at about the same level in both arms. If the level 
of the mercury in the short arm is still below the upper 
edge of the horizontal part of the tube, add a little more 
mercury. If too much air has been allowed to escape, tip 
the apparatus to the right and let some air run in. Work- 



BOYLE'S LAW. 187 

ing in this way, get the level of the mercury in the short arm 
above the curve, and the mercury in the long arm from 1 
to 3 cm. higher. Then read the position of the top of the 
meniscus of each mercury-column on its scale. Place the 
funnel again in the top of the tube, and carefully pour in 
mercury until the level of the column in the long arm has 
been raised about 15 cm. Remove the air-bubbles and 
again read the heights in both arms on the scales. With 
the same precautions add another 15 to 20 cm. height to 
the long-arm column. Again read the levels. So proceed 
till the difference in the levels of the columns in the two 
arms is about 75 to 85 cm. Again read the barometer, and 
if you find any difference in the barometer-readings before 
and after these operations, use the average of the two. 
Read the thermometer, and if you find a small change in 
temperature, average the readings; if a large change, report 
the fact at once. During the progress of the experiment, 
watch the thermometer and note any change of tempera- 
ture. Now you have the following data : 

(a) Barometer-reading before and after. 

(b) Thermometer-reading before and aftei 

(c) Levels of mercury in the short arm. 

(d) " " " " " long " 

Arrange (c) and (d) in a table as follows: 



Height in Short Arm. 


Height in Long Arm. 


No. Trial. 









188 



DYNAMICS. 



Calculation. — Arrange the results of the calculation in 
a table of five columns, as follows: 



Volumes. Pressure. 


Whole Press. 


Ratios of Vol. 


Ratios of Press. 













The figures in column 1 are obtained from the card 
attached to the apparatus, the volumes in cubic centi- 
meter corresponding to each reading on the short-arm 
scale, The higher the number on the scale the less the 
volume of air represented. The figures in column 2 are 
obtained by subtracting the readings of the short arm from 
those of the long arm. The figures in column 3 are ob- 
tained by adding to each number in the second column the 
height of the barometer in centimeters. This gives the 
total pressure of mercury in centimeters. The figures in 
column 4 are obtained by dividing each volume in turn by 
the smallest volume. The figures in column 5 are obtained 
by dividing each pressure (column 3) in turn by the small- 
est pressure. Carry out both these ratios to the second 
place of decimals. 

Questions. — 1. Is there any law as regards the ratio of 
the volume to the pressure of a gas, the temperature being 
constant ? 2. If so, what is it ? 3. Why read the barome- 
ter twice ? 4. Why read the thermometer twice ? 5. What 
keeps the mercury from completely filling the small arm ? 
6. Is it of the nature of a push ? 7. Is it a force? 8. What 
is the name of that force ? 9. In this experiment what is 
the stress? 10. In this experiment what is the strain'? 
11. What sort of elasticity has a gas? 12. What princi- 



SPECIFIC GRAVITY WITHOUT SCALES OR WEIGHTS. 189 

pies, learned in previous experiments, have you made use 
of in this one ? Plot a curve from the data. 



EXERCISE 12. 

SPECIFIC GRAVITY WITHOUT SCALES OR WEIGHTS. 

EXPERIMENT 1. 

Apparatus.— Suspended meter-stick; two stones or other bodies 
of about equal weight; cords; vessel of water. 

Object. — To determine the specific gravity of a solid by 
the principle of moments. 

Manipulation. — Call the body whose specific gravity is 
to be determined A, and the other B. Suspend A about 
25 cm. from end of the meter-stick, Fig. 97, having the 
loop of the suspending 
string tight enough not to 
slip during the experiment, 
Slide the weight along un- 
til it balances A, and note 
its distance from the sup- 
port S. Bring a vessel of 
water under A, and when 
A is completely submerged, 
and clear of the sides and 
bottom of the vessel, move 
B until it balances it again, and note its distance from S. 
You have now the data for determining the specific gravity 
of A. 

Calculation. — In Fig. 97 aS represents the weight in 

air, bS represents the weight in water; so aS — bS or ab 

aS 
represents the loss of weight, and specific gravity = — j-. 




190 



DYNAMICS. 



In 



EXPERIMENT 2. 

Apparatus.-Long spiral spring; meter-stick; clamp; body whose 
t> r specific gravity is to be deter- 

mined ; vessel of water; string 
or wire. 

Object.— To determine the 
specific gravity of a solid body. 
Manipulation. — Note 
length of spring, with sus- 
pended wire only attached, 
Fig. 98, C. Attach the body 
to the lower end, as in Fig. 98, 
A, and record the length of 
spring. Bring the vessel of 
water under the body, immerse 
the body with the usual pre- 
cautions, and again record the 
length of the spring B. 

Calculations. — Reading of 
reference-marks : 

Spring alone = 

With body attached = 

Body immersed = 

ac represents wt. in air. 

ab " « " water, and 

ac — ab represents loss of wt. 

in water, and 
Specific gravity — 

ac _ ac 
ac — bc~ be 
same way find specific gravity of some liquid. 




Fig. ! 



LIGHT. 
EXERCISE 1. 

FOCI OF LENSES. 

Preliminary. — When the light from a luminous body- 
passes through a double convex lens, the point at which 
all the light is concentrated is called the focus of the lens. 
The distance from the centre of the lens to the focus is 
called the focal length. The following exercise investigates 
the effect on the focal length of the distance of the object 
from the lens. The apparatus shown in Fig. 99 is used. 




For the luminous object near the lens we use a light A, 
represented as a candle mounted upon a block C" , which 
slides upon the meter-stick M. The lens L and the screen 
8 are similarly arranged. The position of the lens can be 
so adjusted that the image of A falls on S when A is at 
different distances from the lens, and the distances AL and 
LS can be read on the meter-stick. 

EXPERIMENT. 

Apparatus.— As in Fig. 99, so arranged that an image of an object 
at a considerable distance may be obtained. 

Object. — To study the effect of the distance of the ob- 
ject from the lens on its focal length. 

191 



192 



LIGHT. 



Manipulation. — Bring the outer ends of blocks C and 
C" even with the ends of the meter-stick. Light A, place 
it in the centre of block C", and move the lens to a point 
about 20 cm. from A. Slowly slide the block C towards 
8 until a position is found which gives a sharp image of 
A on the screen. Record the readings of the right-hand 
sides of 8 and D and of block C" (in this case, 0). Move 
the lens towards S until the image is lost, then slowly move 
it back towards A until a sharp image is again obtained, 
and take the reading of D as before. Gently slide block 
G" 10 cm. nearer the lens, and repeat. So continue at in- 
tervals of 10 cm. until an image can no longer be obtained. 
To test the case when the object is as far from the lens as 
possible, extinguish the light and remove it, together with 
block 0". Arrange the rest of the apparatus so that the 
light from some distant object * can pass through the lens 
and fall upon the screen. Find as above the position of 
D that gives a sharp image. Record as follows: 



Read, of S. 


Read, of D. 


Read, of A. 




R. 


L. 


Av. 











In the first and third columns place the readings of right- 
hand sides of C" and 8, respectively. In the second col- 
umn R and L are the readings of the right-hand side of D 
when moved from the right or from the left to the posi- 
tion giving a sharp image. 

Questions. — 1. Is the distance of the lens from the 

* The distance of this object, which should be over 30 meters from 
the lens, should be recorded, whether measured or estimated by the 
eye. 



FOCI OF LENSES. 



193 



screen the same whatever the distance of the luminous 
object from the lens? 2. What other inferences can you 
draw from the results of the experiment ? 

When the object is so distant that the rays of light from 
it are practically parallel where they strike the lens, as in 
the case of the distant object in the experiment, the dis- 
tance from the centre of the lens to the image is called the 
true focal length of the lens. When the object is so near 
the lens that the rays of light are not parallel, this distance 
is called the conjugate focal length. 

Corrections. — In order to make any exact comparisons, 
it is necessary that the true positions of A and of the lens 
should be determined. To get the true position of A, add 
one half the length of block C" to the readings of A in 
Table I. For the position of the centre of the lens add 
one half the width of the board D to the average readings 
for D in the same table. Kecord as follows : 



True pos. A. 


True pos. L. 


Pos. S. 


Dist. AL. 


Dist. LS. 













Calculation". — Taking the first case, express the frac- 
tion —r^r as a decimal carried out to four significant fig- 
A L 

ures. Express the fractions -^-^ and .= T - — * in the 

r LS Focal length 

same way. Do the same for the other cases. Tabulate as 

follows : 



* As obtained in the trial with the distant object. 



194 



LIGHT. 

TABLE III. 



AL 


1 
LS 


Sum of the two. 


1 
F.L. 











Questions. — 1. From the study of Table III can you 
make out any relation between the distance of the object 
from the lens {AL), the conjugate focal length (LS), and 
the true focal length of the lens ? If so, letting F = true 
focal length, f= conjugate focal length, and D = the dis- 
ance of the object from the lens, express your inference as 
a formula. 

EXERCISE 2. 

DISTANCE AND INTENSITY OF LIGHT. 

Preliminary. — By the intensity of light is meant not the 
brightness of the source of light itself, as a lamp-flame, 
white-hot carbon, etc., but the degree to which its light 
illuminates a given body. It is a well-known fact that the 
illuminating power of alight decreases as the distance of the 
illuminated body from it increases. The light from a large 
lamp and from a candle may be of equal intensity if the il- 
luminated body be much nearer to the candle than to the 
lamp. The following exercise investigates the effect of dis- 
tance on intensity of light, with a view to seeing if any fixed 
relation can be made out between them. In order to do 
this, we determine the distances at which lights of different 
known powers give light of the same intensity. For this 
purpose we use an instrument called a Bunsen Photometer, 
whose operation is based upon the fact that when a piece of 
paper having a paraffine spot in the centre is equally lighted 
on both sides, the spot can no longer be seen. The form 
used is shown in Fig. 100. The lights are placed upon the 



DISTANCE AND INTENSITY OF LIGHT. 195 

blocks G and E and the paper upon the block B. All the 
blocks slide upon the meter-stick. For lights of different 
intensities we use different numbers of candles, assuming 
that two candles give twice as powerful a light as one. 
Taking lights of different intensities, and finding the dis- 




Fig. 100. 

tance from each light to the paper when the paper has 
been placed so that the spot in its centre is no longer visi- 
ble, we have the distances required for the different lights 
to give the same degree of intensity. 

EXPERIMENT. 

Apparatus.— Bunsen photometer, as in Fig. 100; 5 candles, 3 or 4 
in. long; matches; scissors for trimming candle-wicks. 

Object. — To see what relation exists between the intens- 
ity of a light and its distance from the lighted object. 

Manipulation. — Arrange blocks G and E at the ends 
of the meter-stick, as in the preceding exercise. Place 
one lighted candle on the block G and one on block E. 
Move the block B towards 6', watching it from that side 
until the spot shows plainly; then slowly move it away 
until the spot just disappears. Have the eye about level 
with the spot, and the line of sight at an angle of about 
30° with the meter-stick. If possible, shield the eye from 
the direct light of the candles by card-board screens. Read 
the position of the right-hand side of D. Xext looking at 
A from the left-hand side, move B within 20 cm. of E; 
then back towards O until the spot just disappears. Re- 
cord the reading of D. Move B within 20 cm. of G, and 
again determine the position where the spot is invisible 
when looked at from the right-hand side, as in the first 
case. Working in this way from each side alternately, 



196 



LIGHT. 



make about ten readings in all. During the operation keep 
the candle-flames burning evenly, trimming the wicks if 
necessary.* In order that the effect of a variation in flame 
may be still more reduced, it is advisable to change the 
candles end for end of the apparatus, moving blocks and 
all. If this be done, take twelve readings in all. Repeat 
these readings first with two and then with four candles on 
C, setting the candles about 1 cm. apart in a line at right 
angles to the length of the meter-stick. Tabulate results 
as follows: 

TABLE I. 



Reading of B. 


Pos. of Centre of L. 


Pos. of Centre of U. 


R. 


L. 


Av. 













Calculation. — The readings for B are practically cor- 
rect. The positions of the centres of the candles are found 
as in the preceding exercise. Eecord corrections as follows: 



Inten. of L.\ 


Inten. of L'.t 


Dist. LD. 


Dist. L'D. 











The numbers in the last two columns are the distances 
from the centres of the candles to D. 

Questions. — 1. How would the distances compare if 
nine candles were used ? Sixteen ? Twenty-five ? 2. Can 
you make out any uniform relation between the distances 

* To protect the caudles from draughts, lamp-chimneys may be 
placed over them, supported, of course, so that air may enter from 
the bottom. 

f That is, number of candles used in each case. 



RADIATION OF LIGHT. 197 

and the intensities ? If so, using I and /' for the intensi- 
ties and D and D' for the distances, express your inference 
as a formula. 

EXERCISE 3. 

RADIATION OF LIGHT. 

Preliminary. — It is generally known that light radiates, 
or spreads out in every direction, from a luminous point. 
The following exercise investigates the effect of distance 
from the light upon the degree of radiation. The light 
from a luminous body is allowed to pass through a small 
opening, and the degree to which it spreads is determined 
by letting it fall upon a screen whose distance from the 
light may be varied. 

In order that the light should radiate from as nearly a 
point as possible, the light is placed in a box with a small 
hole opposite the flame on the side towards the screen. 

EXPERIMENT. 

Apparatus.— As in Fig. 99, the lens being removed and a piece of 
paper with a hole 2 cm. square tacked over the hole in Z>; a box 
fitted to hold the light; ashortmm. scale; sharp pencil; some pieces 
of writing-paper about 3x3 in., one of which is pinned on the screen 
at the beginning of the exercise. 

Object. — To see if there is any uniform relation between 
the degree of radiation and the distance from the point of 
radiation. 

Manipulation. — Light the candle and adjust the block 
supporting it so that the reading of the opening in the box 
through which the light passes is 5 or 10 cm. on the scale.* 
Place D 25 cm. and 8 35 cm. from the hole. If the light 
is properly adjusted, a well-defined square of light will be 
thrown on the screen. Holding the screen firmly, place a 
ruler upon it, and with a sharp pencil rule a vertical line 2 

, * One method of doing this would be to hold the ruler firmly 
against the side of the box facing the screen, and adjust so that the 
right-hand edge of the ruler would come on the 5 or 10 cm. mark 
on the meter-stick. 



198 



LIGHT. 



or 3 cm. long on the left-hand edge of the square of light, 
using great care to get the lines exactly on the edge. 
Mark the right-hand edge in the same way. Set the screen 
40 cm. from the hole, and rule two more lines. So proceed 
up to 60 cm. from the hole. Remove the square of paper 
pinned on the screen, pin on a fresh square and get an- 
other set of lines, working back from 60 to 35. Get four 
sets of lines in all, working back and forth twice. Meas- 
ure carefully on all four pieces of pieces of paper the dis- 
tance between the pairs of lines obtained for each position 
of the screen. Record as follows : 



Pos. of Point. 


Pos. of Screen. 


Dist. between Lines. 


1st. 


2d. 


3d. 


4th. 


Av. 

















From these results calculate 

TABLE H. 



Dist. from Point 
to Screen. 


Increase. 


Av. Width of 
Square of Light. 


Increase. 











In the first column place the reading of the screen 
minus the reading of the left-hand side of the box. The 
figures in the second column are obtained by getting the 
differences between the different readings of the screen. 
In the third column place the average values obtained from 
Table I for the distance between the pairs of lines corre- 
sponding to each position of the screen, and in the fourth 
column obtain the differences in the same way as indicated 
for the second column. 

Questions. — 1. What inference can you draw regarding 



CANDLE-POWER BY TEE RUMFORD PHOTOMETER. 199 



the relations of distance and degree of radiation ? 2. If 
D and D' be any two distances, and / and 1' the corre- 
sponding intensities, can you combine them in a formula ? 
Remember that for each distance the same amount of light 
will spread over a surface whose area would be proportional 
to the squares of the width of the square of light, and that 
the intensity of the light will become less in proportion to 
the surface illuminated. 

EXERCISE 4. 

CANDLE-POWER BY THE RUMFORD PHOTOMETER. 

Preliminary. — The unit used in comparing the light-in- 
tensities is called one candle-power, written c. p. Candle- 
power is measured by determining the distances at which 
the source of light to be tested, and a standard candle 
specified by law,' give lights of equal intensity. For ex- 
ample, if the light to be measured and the standard candle 
must be at the same distance in order to give light of 
equal intensity, the light of required intensity would be 
1 c. p. 

The form of photometer used in this exercise is shown 




Fig. 101. 

in Fig. 101, and is called the Rwnforcl Photometer. Two 
meter-sticks MM carry two blocks LL', one of which 
supports the standard reference-candle, the other the light 
to be measured, represented here by two candles. These 



200 



LIGHT. 



blocks can be moved to any position on the meter-sticks. 
A card-board screen S' is placed between them, and an up- 
right rod R at the left-hand ends of the meter-sticks. Each 
light will cast a shadow from this rod upon the screen at 
the left. When these shadows are equally black, both lights 
are of equal intensity at the screen. 

EXPERIMENT. 

Apparatus.— Rumford photometer as in Fig. 101; candle; light to 
be tested ; scissors. 

Object. — To determine the candle-power of a light by 
the Rumford photometer. 

Manipulation. — Place one candle on block Z/, light it, 
and set the block 30 cm. from the rod. Place on L the 
light to be tested. Allow the lights to burn for a few 
moments, and then move L towards the screen until the 
two shadows cast by the rod are equally dark. Read the 
position of the right-hand side of L. Move L towards the 
screen until its shadow is decidedly the darker (recollect 
that the shadows cross), then move it towards the right 
until the shadows are equal, and again record the reading 
of L. Move II 10 cm. nearer R and repeat. Repeat again 
with L' 10 cm. still nearer. Record as follows: 



Pos. of U. 


True Pos. of 
Candle. 


Po 
EL 


s. of 
L. 


L. 

A v. 


True Pos. of 
Light.* 


Dist. from 

Screen to* 

Candle. 


Dist. from 

Screen to 

Light, 



















Calculation. — Using the formula of Ex. 2, all the 
values are given in the table above, except the intensity 
of the light to be tested, the intensity of the candle L' 
being taken as 1 c. p. Substitute these values for each 
case, taking the intensity of the light to be tested as X. 
Average the values so obtained, and put them down as 
candle-power. 

* Distances of L and L' from rod, plus distance of rod from screen. 



SOUND. 
EXERCISE 1. 

CONDITIONS AFFECTING PITCH. 

Preliminary. — The following exercise investigates the 
conditions affecting the pitch of the note given by the 
vibrating wire. For this purpose the apparatus shown in 

w- 





Fig. 102. 

Fig. 102 is used. The wires WW of different sizes are 
stretched by the balances BB\ the lengths used being 
those between the triangular blocks CC. In order that 
the tension may be the same for different lengths, a fifth 
block, D, may be placed under the string, the wire being 
pressed down on D by the finger H, as shown in the figure. 
Cords cc wound around nails aa hold the balances at any 
desired tension. 

EXPERIMENT. 

Apparatus.— As in Fig. 102. Meter-stick. 

Object. — To observe the effect of (a) length, (b) tension, 
(c) size, on the pitch of the note given by a stretched wire. 

Manipulation. — Part 1. The apparatus being arranged 
as in Fig. 102, hold balance B in the left hand, take a turn 
of the cord c around the right-hand nail a, steadily pull to 
the left on B, and at the same time pulling the cord with 
the right hand until B reads 8 lbs. Eemove the left hand, 
and let the whole strain come upon the cord. Make the 
cord fast by four or five crossed turns around both nails. 

201 



202 



SOUND. 



If the cord stretches so that the tension drops below 8 lbs., 
the operation must be repeated. In like manner put W 
under the same tension. Bring D close to the left-hand 
block C; measure the length of wire between D and right- 
hand block by laying the meter-stick on the blocks parallel 
to the wire. Press the finger on the wire to the left of D, 
as at H in Fig. 102, and sound W. Shorten W by moving 
D to the right, and look for positions that give the first and 
second octaves of the note first obtained, measuring the 
length in each case. Move D back to its original position, 
and calling the note given by W " do " on the scale, look 
for positions giving the other notes in the gamut. If pos- 
sible, carry these measurements through the second octave. 
Repeat, starting with a different length. Record as follows: 

TABLE I. 



Tension. 


Length. 


Note. 









Part II. Remove D, sound W, and change the length 
of W so that it gives the same note as W. Then find what 
tension on one half-length of W will give the same note as 
W. The note given by W is simply used as a reference ; 
hence the length of W need not be recorded. Shorten W 
10 cm. by moving the block D, again set B at 8 lbs., and 
repeat the whole operation. Do this for several lengths, 
and record. 

TABLE II. 



1st Tension of W. 


Tension of W for same 
Note on JiaZ/-length. 


Note that ?Mo/e-length 
of W would give.* 









* See Part I. 



VELOCITY OF SOUND. 



203 



Part III. With a tension of 8 lbs. on each string, and 
with equal length of wire, compare the notes. Do this for 
several lengths and tensions. Eecord 
table m. 



Length W. 


Length W. 


Tension TFand W. 


Pitch of note. 











Questions. — 1. Can you make out any relation between 
the length giving any note and that giving its octave? 
2. Do the lengths giving the note on the scale bear airy 
definite relations to the length giving the first note ? If 
so, what ? 3. Can you make out any connection between 
tension and pitch ? 4. Between size and pitch ? 5. Name 
some musical instruments in which these principles are 
used, and explain how they are applied. 

EXERCISE 2. 

VELOCITY OF SOUND. 

Preliminary. — In the following exercise the velocity of 
sound is determined in two media — air and carbon dioxide. 
The method used is based upon the fact that if a tuning- 
fork be sounded at the mouth of a tube closed at one end, 
the length of the air-column which will reinforce the sound 
of the fork is one quarter the wave-length. By using 
a fork of known number of vibrations, and finding by 
trial the length of air-column which will respond to the 
fork, the velocity may be calculated. 

EXPERIMENT. 

Apparatus. — Resonant tube ; tuning - fork ; wash - bottle with 
water ; chemical generator ; marble ; muriatic acid ; meter-stick ; 
blocks of wood to support generator ; thermometer. 

Object. — To determine the velocity of sound, (a) in air, 
(Jb) in carbon dioxide. 



204 



SOUND. 



Manipulation". — The tube being placed upon a firm 
surface, sound the fork holding it horizontally over its 
mouth, one prong directly above the other. By means of 
the wash-bottle, run water into the tube until the point of 
strongest reinforcement is found. When this point is ap- 
proached, add the water very cautiously, holding the deliv- 
ery-tube of the bottle close against the sides of the tube, 
taking care to wet the sides of the tube as little as possible. 
Place the meter-stick against the inner wall of the tube, 
and measure the distance from the level of the water to the 
top of the tube. Pour out some of the water and repeat, 
making four or five trials in all. Empty the tube com- 
pletely, and support the generator on blocks so that the end 
of the delivery-tube reaches nearly to the bottom of the 
tube. Pour about 20 cm. of acid into the generator and 
allow it to run for three or four minutes; then proceed as 
above. Eecord the temperature. Tabulate : 



Substance used. 


Length of air-column. 


Average. 









Calculation. — Average separately the values of the 
quarter wave-length obtained for air and for carbon di- 
oxide. By substituting these values and the number of 
vibrations of the fork in the formula 
V = No. of vibr. X 4 (length of air-col. -f- J diam. of tube) 
calculate the velocity of sound in each medium. 



APPENDIX A. 



GENEKAL SUGGESTIONS. 

The following suggestions are based upon the author's experi- 
ence in endeavoring to economize the pupil's laboratory time, and 
to reduce to a minimum the labor of supervision, correction, etc. 

Notes.— The note-book should be the original record of the 
pupil's work, and should show his failures as well as his successes. 
He may be allowed to draw his pencil through anything which he 
does not care to have taken into account by the instructor, but 
the use of an eraser should be prohibited. He should be com- 
pelled to record in the note-book all data as fast as obtained. 
The use of scraps of paper for notes, and all trusting to memory 
until after the exercise is completed, should be peremptorily for- 
bidden. 

If the notes of all the pupils are uniformly arranged, the labor 
of the instructor in looking them over is much lightened. A 
convenient arrangement is the following : 

1. Object. As in the manual itself. 

2. General Method. A brief account, in general terms, of the 
principle upon which the experiment is conducted. It should 
state (a) the body experimented upon, (6) the conditions under 
which it was placed, and (c) the proposed observations or meas- 
urements.* 

3. Special Method. A brief description of the manipulation, 
accompanied by a diagram of the apparatus. 

4. Results. A careful record of observations of the results of 
working up numerical data. 

5. Inferences. Whatever general truths the pupil has gath- 
ered from the study of his results. 

6. Remarks. Under this head would appear statements of 
errors with means of avoiding them, possible reasons in case of 
failure, or any other information that the pupil may desire to lay 
before his instructor. 

* See Electricity, Exercise 5; Mensuration, Exercise 2. 

205 



206 APPENDIX A. 

To get the pupil into the habit of arranging his results method- 
ically, and to make the records more uniform, the arrangement 
of the data is indicated in many cases in the preceding exercises, 
and the forms of tables are generally given. A good rule for 
the arrangement of notes is: Everything written out of the lab- 
oratory to be in ink, everything written in the laboratory to be 
in pencil; all written work to be placed on the right-hand page, 
all numerical data, calculations, and diagrams on the left-hand 
page. The handiest form of note-book measures about 8x10 
inches, and contains about two hundred pages. 

Previous to the exercise the pupil should record, in ink, the ob- 
ject and the general method. From a study of the instructions he 
should also provide his note-book with blank tables, diagrams, 
etc., so that the recording of results will require a minimum of 
time. For example, in Exercise 3, on magnetism, diagrams of the 
apparatus without the compass-needle may be made, and that 
may be rapidly sketched in after its deflection has been observed. 

It is highly desirable that the instructor get a general idea of 
each pupil's recorded work before he leaves the laboratory. If 
practicable, the instructor should look over the laboratory en- 
tries as soon as they are made, and if they will pass, the pupil 
should then draw what inferences he can. These should also be 
immediately entered and shown to the instructor. Some sort of 
a check-mark, made at the time to show that this preliminary in- 
spection has been done, will be found convenient when the fin- 
ished note-books are subsequently corrected. At another time, 
before or after class discussion of errors, the pupil's individual 
mistakes may often with advantage be reviewed with him. The 
books so written up should be handed in at stated intervals and 
corrected by the instructor. 

Essays. — From time to time papers on various completed ex- 
periments, beginning with the simpler, may be assigned to the 
pupils, read before the class, criticised by the members, and after- 
wards corrected by the instructor. The object of this work would 
be to train the pupil in explaining briefly, clearly, and minutely 
the steps by which his knowledge was obtained, to give these steps 
in their order, and to prepare a clear description of the apparatus 
used. 

Lectures. — In addition to the regular work, occasional suitably 
illustrated talks on the practical application of physics, particu- 



GENERAL SUGGESTIONS. 207 

larly in the departments of electricity and heat, are interesting 
and generally profitable, especially if they can be accompanied 
by visits to places where the application is made on a commercial 
basis, as, for example, to an electric-light station or an engine- 
room. 

Preparation of Laboratory Work. — The instructions in the 
body of the book assume that the parts of the apparatus are set 
out before the pupils come into the laboratory. The pupils are 
then expected to connect the different parts, and arrange the 
whole in accordance with the diagrams. The diagrams are inten- 
tionally made in conventional form, with the usual signs for the 
various pieces of apparatus. Occasionally two different signs for 
the same piece are used interchangeably. Pupils should be 
taught to use conventional signs in their note-books. 

Apparatus. — Probably the most satisfactory way of getting a 
laboratory equipment is to buy the standard pieces of apparatus, 
as thermometers, spring-balances, scales and weights, and to 
personally supervise the construction of the remainder. For 
those desirous of following this plan instructions are given in 
Appendices B and 0, and, wherever possible, the dealers are indi- 
cated from whom such pieces of apparatus, in whole or in part, 
or their equivalents, may be procured. In some cases temporary 
substitutes for pieces of apparatus arc described. 

Pupil's Preparation. — In order that the laboratory work shall 
be performed methodically and rapidly, the instructor should 
satisfy himself that the object, the method, and the manipulation 
of the exercise have been thoroughly grasped by the pupil before 
the laboratory work begins. This point is a sine qua non. 

Teacher's Preparation. — In working through these experi- 
ments, for the first time at least, it is highly advisable that the 
teacher read over the instructions and notes in Appendix D, and 
perform the experiment himself. In this way he will gain a 
knowledge of the conditions under which the pupils work, and of 
their probable mistakes and difficulties, which will make the hand- 
ling of a laboratory section much easier. The best substitute for 
this plan would be to get some bright member of the class to work 
through the experiment and subsequently talk over his experience 
with him. A trustworthy pupil so prepared is often of consider- 
able aid in acting as an assistant during a laboratory exercise. 

Cost. — The author's experience leads him to think that, where 



208 APPENDIX A. 

the standard pieces of apparatus are purchased, the regular car- 
pentry and metal work done by mechanics, and the remainder of 
the apparatus constructed with no expense except for raw mate- 
rial, the cost of laboratory equipment would approximate to 
$15.00 for each pupil in a laboratory section. The details given 
in Appendices B and C are intended to enable a teacher to make 
a close estimate for his particular circumstances. 

Size of the Sections. — The writer prefers sections of about 
fifteen, all being given the same exercise with individual pieces 
of apparatus — except in a few cases where two exercises are 
worked by half -sections, or by several students together, as indi- 
cated in Appendix D. He has handled larger sections ; and is 
of the opinion that if pupils have been thoroughly prepared, fairly 
successful work can be done with a section of twenty, especially 
with the aid of a pupil assistant. 

Glass-working. — Instructions for glass- working are given in 
the appendices of most chemical and physical manuals. A method 
of cutting large bottles and tubes which is not usually given is as 
follows: Thoroughly soak some common cotton string in water. 
"Wind this wet string smoothly and evenly for a distance of three 
or four inches on either side of the line that is to be cut, the 
place where the cut is to be made being left uncovered for a 
width of about one-eighth inch. In this open space, which 
should be dry, make a scratch with a sharp three-cornered file, 
and heat this scratch over the Bunsen burner. Usually, after 
heating a little while, the glass cracks at the scratch, and breaks 
away in a clean cut all around. Some practice is needed to be 
able to tell when the glass has been heated enough. 

The Edison Current. — There are a number of experiments 
illustrating some of the most important modern applications of 
electricity, which are usually difficult to perform, because they 
require a comparatively heavy current, and call for an expensive 
battery outfit, with its attendant evils. For this class of experi- 
ments and in other suitable cases the author has used the 110- 
volt Edison incandescent-lighting circuit. The arrangement of 
the wiring he adopted is shown in Fig. 103. The positive, nega- 
tive, and neutral wires are all led into the laboratory. 

The positive wire goes first to a rheostat E, and then to a 
double-contact plug-switch S. From one half of this switch, a, 
it passes to the lecture-table, to which the negative and neutral 



GENERAL SUGGESTIONS. 



209 



wires are also led. From the other half of the switch, b, it ex- 
tends along the wall at the back of the pupils 1 benches, and the 
negative runs parallel to it, about eighteen inches below. These 
form the pupils' circuit. With one contact on the switch the in- 
structor can get the positive with the rheostat, and either the 
neutral or negative. With the other contact pupils can get the 
positive through the rheostat and the neutral. At suitable inter- 
vals in the pupils' circuit "single-pole cut-outs, C, in which 
lamps are placed, are attached to the positive wire. From these 
a wire leads to a switch >S", and thence terminates in a binding- 
post B. About three inches from this post is placed another, _B', 

Negative 




connected directly with the neutral wire. On closing the switch 
the current passes from positive to neutral, through the appara- 
tus. The plus binding-post corresponds to the positive and the 
neutral to the negative plates of a galvanic cell. The lamps re- 
tard the current so that no piece of apparatus will short-circuit 
and cut out the others, as one of lowest resistance would 
otherwise do, and so that the turning off and on of the current at 
one tap will not affect the current at the others. The rheostat 
need not be resorted to in these cases, the lamps being enough, 
unless a weaker current than that given by one lamp is desired. 
The rheostat is then used, but the current through the various 
circuits will vary if one is turned off or on during the work. 
Owing to its comparatively high E. M. F. (110 volts) the Edison 
current cannot be used in all the exercises. The author uses it 
for Exercises 3, 10, and 11, and for such experiments as are sug- 
gested in the appended list. 

For the experiments usually performed by the instructor heav- 
ier currents can be used, contacts being made between the posi- 
tive and neutral. The lowest resistance advisable in the rheostat 



210 APPENDIX A. 

is 7 or 8 ohms, giving a current of 15 amperes down, according 
to the resistance of the apparatus. The negative wire in the 
lecture-table may be used when two circuits are needed at once. 
When apparatus is connected with the negative and neutral wires 
at the lecture it is placed in series with one or more lamps. 

The rheostat may be such a one as is used in Edison lighting- 
stations, or may be constructed of a number of lamps in parallel. 
Ten 32 C. P. lamps will give a total resistance of about 11 ohms, 
and the current may be reduced by using fewer lamps. If the 
current given by one lamp is still too much, other lamps may be 
placed in series with it, so as to cut down the current still 
more.* All circuits should be well protected by safety fuses to 
guard against short-circuiting. Before using the Edison current 
for experimental work, the teacher should become familiar with 
the method of wiring, the various resistances of lamps of varying 
c. p., etc. In the case of the stronger currents care must be 
used to regulate the current for the apparatus, in order not to 
melt or overheat it. It should also be remembered that the heav- 
ier currents have a tendency to arc on breaking the circuit ; 
hence all circuit-breaking with heavy currents should be done 
rapidly. Care should be used to make all connections with suffi- 
ciently large wire; No. 16 is small enough. 

The above description refers to the Edison " 110-volt" incan- 
descent circuit, and to no other. 

Some of the experiments in which the Edison current will be 
found useful are the following: 

Electro-magnets. 16 c. p. lamp ;t electric motor (model), 7 to 
20 ohms ; induced currents, 100 ohms ; attraction and repulsion 
of currents, 7 ohms ; thermal effect of current, 7 ohms^ chemical 
effects of current, 400 to 500 ohms ; linear coefficient of expansion, 
16 c. p. lamp ; action and reaction, 150 to 200 ohms ; Ampere's 
law, 16 c. p. lamp ; operating model arc-light, 7 ohms ; operating 
model telegraph, 16 c. p. lamp. 

Mercury. — The mercury required for amalgamating, that for 
reversers and mercury-cups, and that intended for other purposes 
should be kept in separate bottles. Special care should be used to 



* See Scientific American, January 1891, for the construction of a simple form 
of lamp rheostat. 

t A 16 c. p. light when hot may be taken as having about 220 ohms resistance. 
Its resistance increases as it becomes cooler. 



GENERAL SUGGESTIONS. 



211 



keep that needed for Boyle's law, indexes, and calibration, clean, 
dry, and unmixed with other metals. * For amalgamating, it is 
advisable to have a large tin pan coated with asphalt paint. A 
table provided with a ledge is useful for work in experiments 
where mercury is used. "When exposed to the air, mercury be- 
comes covered with a scum. To remove this, cut out a circle of 
letter-paper 10 to 12 cm. in diameter, and fold it twice so as to 
make a cone of 60°. With a pin punch the point of the cone full 
of holes, and place it in a dry glass funnel in the mouth of a 
dry bottle. Pour the mercury into the funnel, keeping its level 
nearly up to the top of the cone. The scum will keep on top and 
the clear mercury will run out through the holes into the bottle. 
Caution pupils about getting mercury on gold jewelry. 

TEMPORARY GAS-PIPING. 

Where there are not a sufficient number of gas taps for a sec- 
tion, the arrangement as shown in Fig. 104 may be useful. A 
glass bottle is provided with a cork 
pierced by several glass tubes. This 
cork should be well soaked in melted 
paraffine. One of these glass tubes is 
connected with the gas tap, the others 
with the tubes leading to Bunsen burn- 
ers. In this way one gas tap can be 
made to serve from two to four students. 
If independent regulation is desired, 
the tube leading to each burner may be 
provided with a screw clamp t or some 
similar device. Glass tubing connected 
with short pieces of rubber tubing, will 
serve well for temporary piping. Where 
a branch tap is to be led off, a small 
bottle provided with a glass tube may be 
used. By such devices as these, if the 
laboratory contain but one or two gas 
taps, it is not a difficult matter to provide enough separate 
burners. 

* For arrangement for keeping mercury clean and dry see Sut- 
ton's Volumetric, Analysis, p. 413. 

f See Eimer & Amend's Catalogue, page 165. 




Fig. 104. 



212 APPENDIX A. 

SOME USEFUL BOOKS. 

Chute. Practical Physics. Boston, D. C. Heath & Co. 
Daniell. Principles of Physics. New York, Macmillan & Co. 
Everett. Units and Physical Constants. New York, Macmil- 

lan & Co. 
Hall. Elementary Ideas, Definitions and Laws of Dynamics. 

Cambridge, Mass., University Bookstore. 
Hall & Bergen. Elementary Physics. New York, Henry Holt 

&Co. 
Harvard College. Descriptive List of Elementary Physical 

Experiments Intended for Use in Preparing Students for 

Harvard College. Cambridge, Mass., University Bookstore. 
Hopkins. Experimental Science. New York, Munn & Co. 
Jones. Physical Problems. New York, Macmillan & Co. 
Kohlrausch. Physical Measurements. London, J. & A. Churchill. 
Lodge. Elements of Mechanics. London, "W. & R. Chambers. 
Maxwell. Matter and Motion. New York, D. Van Nostrand 

Co. 
Mayer. Sound. New York, D. Appleton & Co. 
Mayer & Barnard. Light. New York, D. Appleton & Co. 
Pickering. Physical Manipulation. Boston, Houghton, Mifflin 

& Co. 
Shaw. Physics by Experiment. New York, Effingham May- 

nard & Co. 
Stewart. An Elementary Treatise on Heat. Clarendon Press 

Series. New York, Macmillan & Co. 
Stewart & Gee. Elementary Practical Physics. New York, 

Macmillan & Co. 
The advertising pages of the " Electrical "World " contain illus- 
trations of nearly all kinds of machinery involving the practical 
application of electricity. Occasional articles in the " Scientific 
American " also give valuable hints. 



APPENDIX B. 

LISTS OF APPAEATUS. 

The object of this appendix is to place any one undertaking 
this course in possession of such information regarding the 
nature and expense of materials required as will most aid him in 
making an estimate for his individual circumstances and for any 
particular exercises. The lists are arranged by subject, and each 
one enumerates, unless otherwise indicated, all the apparatus 
required by one pupil for all the exercises upon that subject. 
The notes subjoined give approximate statements of the amount 
of material required, and suggestions for practicable reduction in 
total equipment. References have been freely made to certain 
dealers' catalogues, which it would be well to obtain. The prices 
given are catalogue prices, and are usually subject to a varying 
discount, the amount of which can be ascertained of the dealers. 
Since the same pieces of apparatus are often used in several exer- 
cises, items which have appeared in one list are starred in sub- 
sequent lists. Constructed apparatus stands in the list as one 
item, materials being given in the notes. Cross-reference is made 
by means of the number prefixed to each item. Specifications 
which might go into the hands of mechanics are given in English 
units. Wire numbers are B. & S. gauge (see Hall & Bergen, page 
372). 

ABBREVIATIONS. 

E. S. Co., The Educational Supply Co., 9 Hamilton Place, 
Boston. 

E. & A., Eimer & Amend, 205-211 Third Avenue, K Y. 

Gage, A. P. G-age, Boston (Supplementary catalogue, No. 1). 

G. & W., Goodnow & Wrightman, 176 Washington Street, 
Boston. 

E. S. G. Co., The E. S. Greeley Co., 57 Dey Street, N. Y. 

M. B., Metric Bureau, 146 Franklin Street, Boston. 

213 



214 APPENDIX B. 

Ritchie, E. S. Ritchie & Sons, Brookline, Mass. (Catalogue of 
school apparatus ; also special list of apparatus for Harvard Col- 
lege experiments). 

TV., T. & Co., TVhitall, Tatum & Co., 41-43 Broad Street, 
Boston (1891 catalogue). 

MAGNETISM. 

For No. 11, see also Appendix C. 

Apparatus. — 1. Bar-magnet. 2. Piece of steel. 3. Carpet- 
tacks. 4. Pieces of paper, wood, etc.; 3-in. glass rod, E. & A., 
8004. 5. Copper tacks. 6. Piece of window-glass. 7. Iron-fil- 
ings. 8. Iron nails. 9. Block of wood or bottle. 10. Suspen- 
sion stirrup and thread. 11. Compass. 12. Large darning- 
needle. 13. Iron and copper wire. 14. Three soft iron nails. 
15. Shellac. 16. Glass tube. 17. TVooden clamp. 

Notes. — 1. Conveniently about 8 x | xf in., 35 cts. Sub- 
stitute : Tool steel, 12 x £ x £ in., G. & TV., 10 cts. per ft, 
Cut bar in two and magnetize with large magnet, or in the field- 
magnets of a dynamo. Substitute : Large knitting-needle. 2. 
Knife-blade, knitting-needle. 3. Two sizes. 6. Say 3x3 ins. 
7. Coarse and fine (E. & A. "fine powder " best for latter ; 12 cts. 
lb.). 10. About No. 18 wire ; sewing-thread. 11. Common 
cheap form, brass, glass top, paper scale about 1£ in. diameter 
(about 25 cts. each). 13. Say No. 16, 4 or 5 in. 14. Horseshoe 
nails or clinch nails. 17. Extremely useful. For the form re- 
ferred to, see E. & A. cat., No. 8222. 

ELECTRICITY. 

For Nos. 5, 6, 7, 9, 10, 12, 13, 14, 15, 21, 27, 30, see also Appendix C. 

Apparatus. — 1. Five test-tubes : rack or substitute. 2. Bits of 
sheet zinc, copper (tack), carbon (arc, old battery), amalgamated 
zinc. 3. Copper and zinc strips. 4. Iron and lead plates. 5. 
Resistance-box. 6. Reverser. 7. TVheatstone's bridge. 8. Mer- 
cury for amalgamation, mercury-cups and reverser. 9. Dilute 
sulphuric acid and battery fluid. 10. Tumbler cell. 11. Insu- 
lated wire. 12. Galvanometer. 13. Mercury-cups and short 
circuiting wire. 14. Rack with wires. 15. Sensitive galvano- 
meter. 16. Compass.* 17. Iron nail.* 18. Bits of zinc, carbon, 



LISTS OF APPARATUS. 215 

wood, glass, etc.* 19. Carriage-bolt. 20. Iron filings.* 21. 
Mounted coils; 5 yd. g. s. 5 yd. copper, same size, 10 yd. smaller 
copper (Ritchie E. S. Co.). 22. One large electro-magnet is' use- 
ful. 23. Binding-posts. 24. Connector. 25. Water. 26. 
Blocks of wood for supports.* 27. Contact-keys. 28. Bodies for 
measurement of resistance. 29. Clamp.* 30. Sulphate of cop- 
per cell. 31. Bar magnet.* 32. Two electro-magnets. 

Notes.— 1. E. & A. , 8270. W. T. & Co., 2150. Racks, E. & A. , 
p. 21 9. "W. T. & Co. , p. 44. Easily made from cigar-boxes. Sub- 
stitute empty tumbler. 3. Sheet copper, say 2" x3"; 20 inches 
No. 18 insulated wire soldered to upper end, joint protected by 
asphalt paint, permanent if not handled by wires. Sheet zinc, 
same size (of hardware dealers), wire as above ; attached by 
punching two or three holes near top, passing one end of wire 
(insulation removed) two or three times, first through one hole 
and then through another, and hammering down hard. Plates 
suitable for this exercise from E, S. Co. 4. Sheet iron and lead, 
size above ; wires attached as above. Substitute large iron nail 
and strip of sheet lead with wire twisted around upper end. 5. 
Regular instrument, Ritchie, Gage, $4.00. If calibrated rack 
with wires, No. 14, is used, but one regular box is needed for the 
laboratory. See App. C and D. 6. E. S. Co., 60 cts. Easily 
constructed. 7. Gage, $4.00. Easily constructed. See App. D. 8. 
For amalgamation, half pound in separate bottle; for cups and re- 
verser, keep another portion dry ; rough estimate, half ounce per 
hole. Chemical dealers. 9. Chemical dealers. Concentrated 
acid in 8-lb. bottles ; 5 cts. per lb., bottle, 25 cts. ; 2 ounces. 
Bichromatic potassium or sodium, chemical dealers ; former, 14 
cts., latter, 25 cts. per lb. 10. The cell used for Harvard College 
Experiments would probably do as well. 11. For connections, 
15 ft. No. 18 copper wire, electrical dealers, 40 cts. per lb., 
150 ft. per lb. 12. Material, wood, 5 sq. ft. ; about 40 ft. No. 
18 insulated copper wire ; three binding-posts. The H. C. form, 
E. S. Co., will serve. 13. Material, wood, 9 sq. ins; two binding- 
posts or block 3" x3" xl", and wood-screw; 6 inches No. 16 
copper wire. 14. Material : meter-stick, see Mensuration, board, 
40" x 6" (li sq. ft.); uprights, 1" x 2" x 8"; 7 feet of german- 
silver wire; 17 feet iron and 50 feet uncovered copper wire, say 
No. 24 (see App. C); 6 inches No. 16 uncovered copper wire ; 
binding-post ; also one Eng. binding-post if possible ; Ritchie E. 



216 APPENDIX B. 

S. Co., E. S. G. Co. Iron wire also of hardware dealers ; rack 
without wires, as for Exercise 44, H. C, E. S. Co. 15. Wood 
for frame ; 12 in. glass rod or tube ; needles ; hair or silk fibre ; 
card ; 2 binding-posts ; wire, 100 ft., No. 28 ; No. required, see 
App. D. 19. Three inch, with nut. 22. Magnetizing model motor, 
etc.; E. & A. 23. E. & A., E. S. G. Co., 7 cts. up. Total num- 
ber according to apparatus constructed. 24. Useful, E. S. G. Co., 
p. 90; Ritchie, E. & A., catalogue No. 5614, 10 cts. Substitute. 
Large binding-post with hole large enough to carry two wires at 
once. 27. E. S. G. Co., pp. 310, 326 (four or more old telephone 
bells). See App. D. 30. Useful in certain cases. See App. 
D. E. S. Co. 30. Porous cup ; E. S. Co. Vessel, sheet zinc, 
solutions of copper sulphate and sulphuric acid. See App. D. 
Whole cell, E. S. Co. 32. E. S. G. Co., G. & W. 

MENSURATION. 

For 5, 9. 13, see Appendix C. 

Apparatus. — 1. Piece of paper with crosses. 2. Meter-stick. 
3. Cardboard circles. 4. Paper for markers. 5. Graduated cyl- 
inder. 6. Body of unknown volume. 7. Eight inches fine wire. 
8. Four or five rubber bands. 9. Burette or equivalent. 10. Un- 
graduated jar or equivalent. 11. Glass tube. 12. Bodies for es- 
timation of length. 13. Scales and weights. 14. Avoirdupois 
weights or 8-oz. balances. 15. Bodies weighing from 1 to 2 
oz. 16. Two beakers (1 oz. or so). 17. Saturated solution cal- 
cium chloride and £ sulphuric acid, or equivalents. Any two 
solutions giving precipitates are suitable. 18. Pencils. 19. 
Water. 20. Corks. 21. Blocks of wood* 22. Tumbler.* 23. 
Test-tube.* 24. Suspension-wire. 25. Wax or parafnne shav- 
ings. 26. Bits of stick caustic potash (E. & A.). 27. Burner or 
equivalent. 

Notes. — 1. Crosses ruled with sharp pencil, 30 to 50 cm. apart. 
2. English on one side, French on the other. Met. Bureau, p. 8. 
Ritchie, 25 cts. Substitute, form of school rule, 12-inch scale one 
side, 30 cm. on the other. Met. Bureau, p. 8. 3. Struck off 
with dividers on stiff cardboard, then cut out with fair degree 
of care; 10, 6, and 4 in. diam. 4. Strips 1x5 in.; writing- 
paper best. 4. E. & A. 6138 (65 c). Substitutes may be con- 
structed. For other sizes, see same catalogue. 6. Stone, elec- 
tric light carbon, vol. 5 or 10 cm. 9. E. & A., 5973. Mohr's 



LISTS OF APPARATUS. 217 

burette, price is according to size. 10. E. & A., 6134. 4x1 
iuch (15 c), all sizes. Substitute piece of tubing about 1 inch 
inside diam., 6 or 8 ins. long, lower end closed with paraffin e 
cork and stuck into hole bored in block of wood. 11. 10 in. xf 
in. intern, diam. is good size. E. & A., 6541, No. 7, for exam- 
ple. Provide cork. 12. Books, tables, blocks of wood, etc. 13. 
Scales, E. & A., 5422* ($1.75). Ritchie, E. S. Co. Weights, E. 
& A., Ritchie, E. S. Co. 14. As used for weighing letters. Com- 
plete equipment, one apiece. Without exercise on friction, one 
to every three students is sufficient. Obviates need of avoirdu- 
pois weights. 16. E. & A., W. T. & Co. 17. In stock bottles 
labelled "No. 1," " No. 2." 

DENSITY AND SPECIFIC GRAVITY. 

Apparatus. 1. Bodies for the determination of density. 2. 
Scales and weights.* 3. Graduated cylinder.* 4. Paper markers. 
5. Beaker.* 6. Wire.* 7. Specific-gravity bottle. E. & A., 
5683; W. T. & Co., p. 15. 8. Liquids and solids for specific 
gravity. 9. Apparatus for liquid pressure. 10. Apparatus for 
specific gravity by balancing. 11. Meter stick.* 12. Funnel. 
13. Apparatus for ex. on floating bodies. 14. Apparatus for 
ex. on atmospheric pressure. 15. Apparatus for specific gravity 
by barometric columns. 16. 8-oz. balance or avoirdupois 
weights* 17. Water. 18. Box. 19. Sinker. 20. Tumbler.* 
21. Clamp.* 22. Vaseline. 23. Wire for suspension. 

Notes. — 1. Rectangular blocks, spheres, etc., irregular body 
(weighing about 50 grm. each) liquid. 8. Small iron ball, 
weight 1£ stone, etc. For liquids, alcohol, saturated solutions 
of calcium chloride, copper sulphate, salt, or equivalents ; oil. 
These may be kept in stock bottles and known by number. 9. 
See App. D. Materials : meter-stick ; * clamp ; * wire ; * sheet 
rubber, druggist (4 sq. ins.) ; thistle tube, E. & A., 6411. W. T. 
& Co., 2201 ; rubber tubing (length depends on vessel used), 
E. & A. ; reference-scale ; vessel for water, pail or equivalent ; 
piece of board for gauge support ; 6 ins. of small glass tube. 
10. Material : 2 large glass tubes about 1 meter long, E. & A., 
6541, No. 5, or for form given in App. C, 6540, No. 15 and No. 
3 ; support, 3x1 ft.* and baseboard. See App. C. ; 8 or 10 ins. 
fine iron wire or a cork ; leather strips. 12. Thistle tube is best. 
13. Small test-tube,* corked, containing shot enough to float 



218 APPENDIX B. 

upright; the whole weighing about 13 grams. 14. Material: 
Barometer tube, 3 ft., E. & A., 6541, No. 5, one end sealed ; 2 
lbs. mercury ; * feather and wire ; meter-stick ; * scales * and 
weights * (up to 500 grams) ; vessel for mercury bath (small 
porcelain mortar or equivalent). 15. Material : small glass 
tubing, E. & A., 6541, No. 4, 6 ft. ; bottle ; 6 in. rubber tubing 
to fit glass tubing ; small glass plug, size of tubing ; fine wire ; 
two vessels for liquids. 18. Starch box or equivalent for support- 
ing scales. 23. Druggists. One bottle lasts a long time. 

HEAT. 

For 15, 31, 34, 36, 38, see also Appendix C. 

Apparatus. 1. Metallic rod. 2. Burner.* 3. Clamp.* 4. Wax. 
5. Pieces of wood and of glass rod.* 6. Large iron nail.* 7. Two 
beakers.* 8. Ring-stand. 9. Wire gauze or sand-bath, 10. 
Potassium permanganate. 11. Thermometer. 12. Ice or snow. 
13. Tumbler.* 14. Boiler with connections. 15. Apparatus for 
testing thermometers. 16. Wooden paddle. 17. Spring balance 
(or coarse scales and weights). 18. Piece of window glass.* 19. 
Timepiece. 20. Pint tin pail. 21. Melting-tubes. 22. Stirring- 
rod. 23. Bodies for melting- and boiling-points. 24. Five test- 
tubes* and corks, one perforated. 25. Mercury* 26. Alcohol.* 
27. Scales and weights.* 28. Iron ball or equivalent. 29. 
Cotton string. 30. Calorimeter. 31. Apparatus for latent heat, 
or substitute. 32. Cardboard screen. 33. Blocks of wood.* 34. 
Apparatus for expansion of gas, or substitute. 35. Meter-stick.* 
36. Apparatus for expansion of liquid. 37. Alcohol. 38. Ap- 
paratus for expansion of solid. 39. Two tin cans. 40. Granulated 
sugar. 41. Powdered sugar. 42. Sand, iodine, copper sulphate. 
43. Incandescent lamp. 44. Water. 45. Dividers. 46. White 
cards. 47. Rubber bands. 48. Three corks. 49. Funnel. 50. 
Watch or clock. 51. Block of wood. 

Notes. 1. Copper, brass, or iron £ in. x 1 ft. Wrought iron 
comes in rods, and may be cut to suitable length, or large elec- 
tric-light wire may be used. 2. E. & A., 5809, common chemical 
form with 2 ft. of rubber tubing. Substitutes. Alcohol lamp, 
E. &. A., p. 165, or glass bottle with perforated cork, carrying 
glass tube for wick. 4. Common yellow wax or paraffine. 7. 
Some form of thin glass vessel which can be heated is called for 
in several of the exercises, and is also used in the form of calor- 



LISTS OF APPARATUS. 219 

imeter described in 30. The best is a chemical beaker ; these 
can be obtained from dealers in chemical apparatus, and usually 
come in "nests." E. & A., p. 61, especially 5550 and 5561 a, 
W. T. & Co., p. 15. The next best substitute is a so-called " hot- 
water tumbler." These can usually be heated on a sand-bath 
without much danger of breaking. If a metallic calorimeter is 
preferred, Part 6 of Exercise 1 might be either performed before 
the class, or with " hot- water tumblers," and the use of the 
beakers omitted altogether. 8. E. & A., pp. 216, 217 ; useful 
form, 8212 ; substitute wooden clamp,* but not as good. 9. 
Reduces breakage if flasks are used. E. & A., 8039 and 8442. 
10. Chemical dealers. 11. Centigrade thermometer reading to 
a little above 100° is preferable. Ordinary Fahrenheit ther- 
mometers could be used. There is made a cheap form of ther- 
mometer which has a paper scale, the whole being enclosed in a 
glass tube. These are commonly graduated both to Fahrenheit 
and Centigrade. A very useful form is a Centigrade chemical 
thermometer reading to 1°, E. S. Ritchie & Sons, $1.00. See also 
the catalogs of dealers in chemical supplies, and that of the 
Educational Supply Co. 14. Pint flask, E. & A., 6344 a, with 
safety tube, cork and delivery tube, or pint tin cans with hole in 
top, fitted to carry cork. Empty " Squibb's ether " cans have a 
hole so fitted, and could probably be obtained at drug stores. 
For general form of delivery tube see Fig. 75, p. 134, and 
Fig. 76, p. 137. (No safety tube shown.) 17. 64-oz. balances 
best ; two or three are sufficient. 24-lb. balances might be used. 
21. Time is saved by giving out ready filled. 22. Made of glass 
rod, E. & A., p. 154. 6 in. glass rod also needed for 5. 23. 
Paraffine, wax, benzine, ether, alcohol. 25. f ounce. 28. 
Cast-iron with hole drilled through them, Gage, Ritchie. Sub- 
stitutes, glass stopper, lead bullet, etc. 30. A form which has 
given good results is made by placing a chemical beaker either 
inside of a larger one, or in a tumbler, and filling the space 
between the bottom and sides of the two vessels with excelsior, 
or some other non-conductor. Another form is a nickel -plated 
"liquor-shaker." E. S. Co. This is less liable to be broken, but 
is somewhat more expensive. Bright tin cups or pails would also 
serve the purpose. 31. Boiler and connections, see 14 ; ring- 
stand, see 8 ; burner, see 2. Material : 5 ft. glass tubing, E. & 
A., 6540, No. 3 ; 2 ins. small rubber tubing for connectors, E. & 



220 APPENDIX B. 

A., p. 199 ; 2- to 4-litre glass bottle. The bottles in which acid 
comes are very suitable. For the bottle might be substituted a 
tin can fitted to carry a cork in the bottom ; 3 ins. large glass 
tubing, E. & A., No. 15 ; 3 corks, one for bottle, two for steam 
trap. At least one litre flask is desirable if students are to fill 
calorimeter. See App. D. For substitute experiment, ring-stand, 
boiler, calorimeter, burner, and blocks. 31. 2x2 ft. tacked to a 
baseboard. 34. Material : 4 ft. glass tubing, vessel of 31; vessel 
for gas (see App. C); cork ; connectors; drop of mercury.* 36. 
Material, test-tube ;* cork ; 2 ft. small glass tubing. 37. Specific 
gravity at average temperature of room previously determined. 
38. Material. 1st method : Jacket ; rod; wood ; 10 cm. scale ; 18 
in. square brass rod, £- in. square ; needle ; thread ; wire for 
rivets ; 2 corks ; glass tubing ; wire Tor guys ; support for short 
scale. (For brass rod, see G. & W., p. 76.) 2d method : 2 
ft. brass rod. I in. diam. ; 2 pieces brass plate (heavy), 2x2 
ins., hardware dealers ; clock-face ; minute-hand ; 6 in. glass 
tubing ; 2 corks ; wood for baseboard, etc. ; 2 ft. large glass or 
tin tube, E. & A., 6540; No. 16 is a good size. 

DYNAMICS. 

For Nos. 1, 5, 8, 10, 11, 14, 17, 18, 21, 22, see also Appendix. C. 

Apparatus.— 1. Apparatus for Exercise 1. 2. 24-lb. spring bal- 
ance.* 3. Board. 4. Blocks for friction. 5. Dynamometer or 
8-oz. balance.* 6. Fish-line. 7. Dividers.* 8. Apparatus for 
composition of angular forces. 9. Meter-stick.* 10. Appara- 
tus for composition of parallel forces. 11. Apparatus for in- 
clined plane. 12. T-square or plumb-line. 13. Apparatus for 
pendulum. 14. Apparatus for collision or substitute. 15. Wire 
of two sizes and two materials. 16. Half spool and screw. 17. 
Apparatus for elasticity of a solid. 18. Apparatus for elasticity 
of a gas. 19. Barometer. 20. Mercury. 21. Spiral spring. 22. 
Hook for Exercise 11. 23. Bodies for determination of specific 
gravity. 24. Timepiece.* 25. 40-cm. scale. 26. Callipers. 27. 
Nails. 28. Clamp. 

Notes. — 1. Material : 10- or 12-lb. weight or loaded box ; 8 or 
10 ft. No. 18 iron wire ; strong screw-eye ; cotton string. 2. One, 
if the last part of Ex. 1 be worked by two pupils. 3. 6 x £ ft. 
Two hard-pine matched floor-boards held by cleats on under side 
are good. Maybe used also in 11 and 14. 4. 3 x 4 x fins. They 



LISTS OF APPARATUS. 221 

may be cut from hard-pine floor-boards, planed on one side, 
screw-eye set into one end of one of them. 6. Smooth cord, strong 
enough to stand 25 lb. pull. About 25 ft. 8. Three students. 
Material. Three balances, see 2 ; one block, see 4 ; dividers, see 
7; cord, see 6; see App. D in connection with the fourth balance. 
10. Three students. Material : meter-stick, see 9 ; cord, see 6 ; 
3 balances, see 2. 11. Two students. Material : balance, see 
2 ; cord, see 6 ; board, see 8 ; carriage (skate, Catalogue of J. K. 
Judd, 1364 Broadway, N. Y.) ; small box ; heavy bodies for 
loading box ; support and rod, or equivalents, see App. C ; 
screw-eye ; meter-stick, see 9. 13. 3 feet cord fine enough to 
fit into slot of screw ; 2 wood-screws ; spool ; iron balls of two 
sizes (see Heat list); for general form of apparatus, see Fig. 91, 
14. Two students. Material : board, see 3 ; meter-stick, see 9 ; 
clamps,* 2 ivory balls, Ritchie, E. S. Co.; 50 ft. No. 30 wire 
for suspension ; 8 cards mounted on blocks 2x3 ins.; elec- 
tro-magnets (old telephone bells, E. S. G. Co., G. & W.); cur- 
rent; circuit-breaker, E. S. G. Co., App. C, small tacks ; board 
for ceiling, 2 x 1 ft. ; screws ; putty. If balls are not weighed, 
scales and weights. Substitute experiment. Three students. 
Material : Board ; 2 meter-sticks ; as above ; 12 ins. No. 18 
spring brass wire, Ritchie ; 2 pint tin pails (see heat); cotton 
string; candle; No. 18 wire for suspension; four screw-eyes; heavy 
bodies ; rough scales. 15. About 25 ft. of each size, breaking- 
weight under 20 lbs. 17. Material : block, 3x3x6 ins.; block, 
1 x 2 x £ ins.; block, 3x3x3 ins.; reading-card with slid- 
ing block ; elastic bands ; meter-stick, see 9 ; scale pan ; 2 
ft. No. 28 wire to support same ; 2 ins. pencil or equivalent ; 
large and small wood-screws; rubber strip, 36 x £ x J ins., 
another, 36 x % x \ ins., E. S. Co. 18. Two pupils may work 
together in order to save mercury. See also App. D. Material : 
mercury, see 20 ; meter-stick, see 9 ; support (see Specific Gravity) ; 
40 ins. glass tubing, E. '& A., p. 155, No. 5 ; 20-cm. scale, see 25 ; 
leather strips ; reading-cards, see Note 17 ; small screws ; feather 
and rod. For calibration, scales, weights, small beaker. 19. 
One in the laboratory. 20. 1 lb. See note 18, and note 14 on 
Density and Specific Gravity. 21. 4 ft. No. 18 spring brass wire 
twisted around a broom-stick. 22. See App. C. 23. Stones, 
weights, etc. 25. For 18 useful in 8 also. Made by sawing up a 
meter-stick. 1 meter-stick required for this to 2 sets apparatus 



222 APPENDIX B. 

for 18.. Substitute in 18, after calibrating put volume scale on 
cardboard and attach to short arm. 26. Useful for determining 
diameter in 13. Substitute, rectangular blocks. 

LIGHT. 

For 1 and 2, see also Appendix C. 

Apparatus.— 1. Apparatus for a, lens work ; 6, intensity of 
light ; c, radiation of light. 2. Rumford photometer. 3. Candles. 
4. Light for determination of candle-power. 5. Scissors. 

Notes. — 1. Material : spectacle lens, 6 ins. focal length ; 
meter-stick ;* baseboard ;* 3 blocks ;* cigar-box ;* white paper or 
cardboard ; wire nails ; candle ; chimney ; corks.* Material : 
6, in addition to above, white unruled paper. Material : c. in 
addition to material required for a, block with perforated 
screen ; arrangement for screening light. 2. Material : base- 
board ;* 2 meter-sticks ;* 2 blocks ;* stiff cardboard for screen ; 
lead-pencil or pen-holder. 4. See Appendix C. 

SOUND. 

For 1 see also Appendix C. 

Apparatus. — 1. Sonometer. 2. Middle C fork. 3. Carbon diox- 
ide generator. 4. Muriatic acid. 5. Marble. 6. Resonant jar. 
.7. "Wash-bottle. 8. Supporting-blocks. 9. Nails. 10. Meter- 
stick.* 

Notes. — 1. Material : 5 ft. Nos. 28 and 30 spring brass wire,* 
Ritchie ; two 24-lb. balances ;* 2 ft. strong cord ;* 4 triangular 
blocks ; baseboard,* 4 ft. x 6 ins. 2. Ritchie. 3. Material : 
wide-mouthed bottle ; safety tube :* 2 ft. small glass tubing ;* 
cork.* See Shepard's Chemistry. 4. E. & A., 8-lb. bottles; 
about 2 ounces per student. 6. Hydrometer jar, 1 ft. x 1 in. 
internal diameter ; E. & A., p. 110, or substitute. 7. Material 
same as for generator. See Shepard's Chemistry, p. 348. 



APPENDIX C. 

CONSTBUCTION OF APPABATUS. 

This appendix contains instructions for the construction of ap- 
paratus. An elementary knowledge of glass-working and the 
simpler carpenters' tools is assumed. If the work be done by- 
regular mechanics, it is well to remember that they have a ten- 
dency to give an unnecessary finish, which increases expense. 

General Laboratory Equipment. — It is convenient to keep 
on hand an assorted supply of cord, iron wire, nails, screws, 
small boxes, etc. Wire should be kept wound upon spools. 
Necessary tools are hammer, screwdriver, cutting-pliers, shears, 
and small hand-drill or brad-awl, and in construction work, a pair 
of tin-shears, jig-saw, cross-cut saw, soldering-apparatus, small 
plane, and quarter-inch chisel. If standards are to be con- 
structed, a good balance, with weights up to 1 K. , burette, set of 
litre, half-litre and quarter-litre flasks and resistance-box would be 
needed. A pair of rough grocer's scales will prove useful. Hard- 
pine floor-boards make good baseboards, etc. ; if tongued and 
grooved, two or more lengths may be joined together. Shellac, 
glue, asphalt paint, and a few large bottles for solutions, etc., are 
needed. 

Wire and Binding-posts. — Probably the best plan would be 
to obtain a pound of No. 18 and of Nos. 28 or 30 insulated wire, 
and of other wires such quantities as may be required in con- 
struction. Binding-posts can sometimes be cheaply obtained 
from old telephone apparatus. Sufficient contact can usually be 
got by screwing the binding-post nearly in, taking two or three 
turns around it with the end of the wire, and then screwing the 
binding-post firmly on it. It is better, however, to solder the 
wire to the post. 

223 



224 



APPENDIX C. 
MAGNETISM. 



Compasses. — For magnetic work alone, substitutes for regular 
compasses are readily constructed. As illustrations, three are 
given. 




Fig. 105. 

I. A support is made of glass tubing or rod bent into the 
form shown in Fig. 105. This is set into a support of wood about 
4 in. square and i in. thick (a piece of a cigar-box for example), 
to which it may be more firmly attached with sealing-wax. From 
this support a magnetized knitting-needle 3 in. long is suspended 
by a hair or fine thread. It is a good plan to weight the needle 
with a bit of sheet lead tied on with waxed thread. 

II. Support of cigar-box wood, as shown in Fig. 106. Base 




Fig. 107. 



3 x 4 in.; supports 3 in. high. Pins driven into the base prevent 
the needle from swinging too far. The needle is loaded and sus- 
pended as in I. 

III. A temporary substitute for a compass may be constructed 
by suspending the needle from the bottom of an inverted tumbler 
as in Fig. 107. The suspending fibre is held to the glass by shoe- 
maker's wax. 



CONSTRUCTION OF APPARATUS. 225 

ELECTRICITY. 

Resistance-boxes. — If one regular box is available, others can 
be constructed by mounting in a cigar-box insulated German- 
silver wire of suitable lengths and sizes. The capacity of this 
substitute may be made less than that of the regular box, but 
bodies of resistance within its capacity must be assigned for 
measurement. The resistance of the wire per cm. is determined 
by measuriug the resistance of four or rive lengths and averaging 
these values, and lengths required to form coils of any desired 
resistance are then measured off. Contact can be secured by 
switches or by some other device, such as the ' ' post-office 
form." * The points for the switches can be made of round- 
headed McGilFs paper-fasteners, set into holes bored in the wood, 
the ends bent apart below, and the coils soldered on as in 
Fig. 108. 




Fig. 108. 

The rack with wires described on p. 231 may be converted into 
a resistance-box by determining the resistance of 1 cm. of the 
G. S. wire. Get the resistance of a number of lengths, and take 
their average value for the resistance of 1 cm. Enter this value 
upon a card attached to the instrument. The total resistance is 
found by multiplying this value by the number of cm. in circuit. 
A scale reading directly in ohms could also be easily made and 
placed upon the apparatus. The capacity may be increased by 
using more G. S. wire. 

Current-re verser. — This instrument is constructed on the 
same principle as the mercury-cups.t In a block of hard pine or 
other suitable wood, 3 x 3 x f inches, bore four half-inch holes one 
half inch deep, whose centres are at the four corners of a square. 
Cut two pieces of ISTo. 16 insulated wire two inches longer than 
the diagonal distance between the centres of the holes, and re- 
move the insulation from each end for about an inch. Twist the 

* See page 133, Stewart and Gee, vol. 2. f See page 230. 



226 



APPENDIX C. 



centre of one piece around the centre of the other for a short 
distance and bend the ends into the general form of an X, as in- 



A±=- 


,_-_,-_, 


_J^\=^l)B £©=7^\ 


,.-.==, 


^ 


S 








S 


B r 


-------= z 


\^=OB B&=k^J/ 




^^=" 



dicated in Fig. 109. Turn the uncovered ends down at right 
angles so as to rest in the holes. Either binding-posts or the 




substitute may be used ; the latter is just as good, as the instru- 
ment is always inserted in the circuit between others. When 




the wires leading to the instrument are connected with two 
diagonal holes, and the wires leading from it with the other two, 
on filling the holes with mercury, and inserting the "X," the 



CONSTRUCTION OF APPARATUS. 227 

current will pass as shown in Fig. 110: on lifting the "X," 
turning it half round, and replacing, it the current will be re- 
versed, and pass as shown in Fig. 111. The ends of the wires 
should be scraped bright before using, or else amalgamated. 
When placing the "X" in the mercury, it should be moved 
around a little before the contact is considered good. The cur- 
rent is reversed for each rotation of 90°. 

Wheatstone's Bridge. (See Fig. 31.) — Make the base-board 
about 14 in. square. Use No. 16 wire or strips of heavy sheet 
brass. No. 18 wires soldered on at the points b and c for gal- 
vanometer, and at e and / for resistance-box connection , would 
reduce the number of binding-posts. The posts at a, d, g, and 
h could also be replaced by the substitutes, as in the construc- 
tion of mercury-cups. 

Battery Fluid. — One formula is : Water, 900 grams ; pulver- 
ized potassium bichromate, 120 grams, or sodium bichromate, 104 
grams ; concentrated sulphuric acid, 200 grams, or 100 cu. cm. 
Put half the water into a vessel of as thin glass as possible, add 
the potassium bichromate, then the acid, with constant stirring 
until the liquid becomes quite warm. If it gets too hot, reduce 
the temperature by adding more water. Keeping the liquid hot 
and stirring it facilitates the solution of the solid. The ease 
with which the temperature can be reduced with water decreases 
the liability of breaking the vessel. The solution may be kept in 
a stock bottle and used until quite green. At the close of each 
laboratory exercise the fluid in the cells should be poured back 
into the stock bottle, and the cells refilled for the next exercise or 
section of the class. 

Tumbler Cell. (See Fig. 13.)— This is a bichromate cell. The 
carbon plates may be made by sawing up the carbons used in the 
"Westinghouse alternating-current arc-light. These come in flat 
strips, 5 or 6 inches long, about one third of an inch thick, and 
2£ inches wide. Carbon, plates may also be obtained of dealers. 
To cut the carbon, fasten a saw having quite fine teeth upside 
down in a vise. Holding the carbon in both hands, rub it back 
and forth rapidly on the saw, bearing down enough to make the 
saw cut. When partially sawed through, the carbon is liable to 
break suddenly at the cut, and care must be taken to avoid lacerat- 
ing the hands on the saw. Drill a hole through the carbon near 
the top. Pass a piece of No. 18 wire, the insulation of which has 



228 



APPENDIX C. 



been removed for 2 or 3 inches, through the hole, and twist the 
end firmly about the main wire until it is pulled up hard against 
the carbon. Dip the top of the carbon in melted paraffine to a 
depth of about half an inch. It is convenient to wind the con- 
necting wires into a spiral. The zinc plates may be constructed 
as follows: To make the mould, cut out of a cigar-box cover a 
piece the size of a carbon plate; lay a square of sheet-iron about 
4x4 in. upon a piece of hard- wood board, place over this the cigar- 
box cover with the cut-out portion removed, and screw or nail the 
three firmly together. Scrap-zinc or old battery-zincs may be 
melted over a Bunsen burner, or better, over a gas stove. After 
the zinc is melted, it should not be left in the ladle very long, as 
it oxidizes rapidly. Take a piece of battery-wire, say No. 18, 
from 12 to 18 inches in length, remove the insulation for about 2 
inches at one end, and bend that end in the form of the letter S. 
Place this end in the mould, as indicated in Fig. 112, so that it 




does not touch the bottom of the mould, and so that it will be 
covered by the zinc. Pour in the melted zinc in a thin stream, 
being careful that no scum passes, until no more can be added 
without overflowing. Leave it in the mould until nearly cold. 
Tip the mould upside down, give it a few raps on the upper side, 
and the zinc will fall out. In handling the plates do not lift them 
by the wire, as it is liable to break off. Size of plates depends on 
size of tumbler, but plates of App. B, 3 and 4, must be same size. 
Soak in melted paraffine some pieces of cigar-box about one 
quarter of an inch wide and as long as the plates arc wide 1 . Lay 
the carbon plate on the table; put one of these pieces of wood 
near one end and another near the other end; place the zinc plate, 



C0NSTRUC1I0N OF APPARATUS. 229 

previously amalgamated, on top, and slip a strong rubber band 
over the two plates to hold them together. Insert the plates in 
the tumbler. In adding the liquid, take care that it does not get 
as high as the points where the wires are attached to the plates. 
Keep the plates out of the solution except when in actual use. 
Directions for the construction of a similar form of cell, in which 
the ordinary round arc-light carbons are used, will be found in 
the Scientific American for May 10, 1890. 

Galvanometer. (See Fig. 16.) — This galvanometer is con- 
structed as follows: The hoop H is a circle of wood 14 in. in 
diameter and 1\ in. thick. Out of it is cut a semicircle as shown, 
11-i- in. in diameter. The outer edge is grooved to hold the wire. 
The support D is a piece of wood 10 x 6 in. and 1J in. thick, 
having cut in it a slot to receive the hoop. The base-board S is 
12 x 10 iu. and 1£ in. thick. Starting at lowest point of the hoop 
and leaving an end of three or four inches, wind the wire 
(No. 18, "Office Wire"') once around, leave a loop, and wind it 
around nine times more. If the hoop is grooved the coil need 
not be secured. If the hoop is not grooved, the coil may be 
bound to the rim by pieces of string passing through holes bored 
in the hoop near the rim. Place the hoop in the support, having 
pulled the ends of the wires up through the slot, in which a small 
groove may be cut if needed. Fasten the hoop in place by 
wedges or glue. Secure the support to the base-board by brass or 
copper nails or screws. Attach the wires to the binding-posts, 
and shellac the whole to prevent warping. The above dimensions 
give an instrument heavy enough to stand firm, and not easy to 
break. A cheaper form could be constructed by making the hoop 
from the top or bottom of a salt -box, securing the coil in place by 
strings, and making the other parts in proportion. The base- 
board should be thick and heavy. As the hoop would be thinner, 
a circle of card-board as large as a silver dollar, fastened in the 
centre of the semicircle cut in the hoop, would form a good sup- 
port for the compass. The only expense of this form would be a 
few cents for the wire, and the cost of the binding-posts. A good 
base for this form is a cigar-box, such as contains 50 cigars, filled 
with small stones and nailed up. A substitute for a compass can 
be made by suspending a magnetized needle from the hoop, al- 
lowing it to hang in the centre. It is not as satisfactory as a 
compass. 



230 



APPENDIX C. 



Mercury Cups. (See Fig. 113.) — Constructed out of blocks of 
hard- wood (hard pine is good), 3x2 in. and | or 1 in. thick. Near 
one end bore two holes, H, half an inch in diameter and half an 
inch deep, and near the other ends place two binding-posts, B. 
Shellac the block and the insides of the holes. Connect the bind- 
ing-posts with the holes by two pieces of No. 16 copper wire, W, 
one end of each piece being fastened to a binding-post, and the 




other running down to the bottom of the corresponding hole, 
where it is bent into the form of a flat spiral. If the wire is 
insulated, the insulation must be removed from the part in the 
hole, and the wire scraped clean and bright. For use, fill the 
holes two-thirds full with mercury. 

The only expense connected with this instrument is that of the 



CONSTRUCTION OF APPARATUS. 



231 



binding-posts. These may be dispensed with by the arrangement 
shown in Fig. 114. Attach a strip of wood \ x \ x 2 in. to the 
top of the block by a single screw. Pass under this strip the 
wires by which the instrument is placed in the circuit by loosen- 
ing the screw a little and then turning it down firmly, scrape the 
ends bright, bend as directed above, and insert them in the holes. 




Rack with Wires. (See Fig. 28).— The base-board A is 5 or 6 
in. wide, and of such length that the centres of the uprights are 
a meter apart. The ends of the meter-stick rest in notches cut 
in the uprights. Small tacks are driven into the uprights, at 
intervals along vertical lines dropped from the ends of the meter- 
stick. From the binding-post a naked German-silver wire is 
carried to the lowest tack on the other upright and back to the 
first upright, as shown. A piece of No. 18 uncovered copper wire 
runs up from binding-post a, and to it are attached the ends of 
the naked iron and copper wire, as indicated. The number of 
lengths of these depends upon the size of wires. For the sliding 
contact, the end of a piece of No. 18 copper wire may be ham- 
mered out flat, and then bent into the form of a hook. An Eng- 
lish binding-post is best. 

Sensitive Galvanometer. (See Fig. 115.) — The frame is of wood 
about 4 x 4 in. ; the support for the needle maybe made of wood 
or glass tubing ; and the needle itself a piece of magnetized 
knitting-needle short enough to swing freely in the frame. A 
piece of writing-paper is cut in the form shown, and the needle 
stuck through the lower part. A second needle, for a pointer, is 
stuck through the upper part. The two needles should be about 



232 



APPENDIX C. 



one inch apart and the lower one only should be magnetized. The 
frame is wound with wire as shown by the dotted lines, with as 
many turns as desired. Space is left in the middle to admit the 




needle, which is then suspended by a hair, or a thread of 
untwisted silk, so that it swings freely within the coil. If 
desired, a scale may be marked on a circular piece of card-board, 
and laid on the coil, but it is not necessary. In the diagram the 
card shown above the indicator swings with it and serves to 
show the motion to a class. If this were used, the indicating- 
needle would not be needed. The whole may be covered with a 
bell-jar, or a large glass bottle whose bottom has been cut off. 

Coils of Wire.— These are made of cotton-insulated wire 
measured off in the lengths indicated in Exercise 4, wound into 
a coil on two fingers and attached to a piece of stiff card-board by 



CONSTRUCTION OF APPARATUS. 233 

paper-fasteners or wire passing through holes in the card and 
around the coil. The number and length of the wire are marked 
on the card, which may then be shellaced to preserve it. The 
ends of the coils are left free for two or three in., and the insu- 
lation removed from these ends. For the 5 and 10 yd. coil, the 10 
yd. are looped in the middle, and then wound so as to leave the 
loop projecting for a few in. The insulation is removed from 
the loop, and it is twisted together ; or, if preferred, they may be 
wound upon spools instead of being mounted on cards, the loose 
ends being drawn through holes bored in the spools. The num- 
bers given in Exercise 4 need not be strictly adhered to, provided 
the cross-section of the german-silver wire corresponds to that of 
the same length of copper wire, that the 5, 10, and 20 yd. of cop- 
per wire are of so small a cross-section as to make the changes in 
the galvanometer readings due to changes in lengths sufficiently 
marked, and that there is considerable difference in the cross- 
section of the two coils of copper wire 5 yd. long. 

Dynamo and Motor. (See Figs. 116, 117.) — The field-magnets 
are provided by a large electro-magnet.* The armature is a 
gramme ring, constructed as follows : A circular disk of wood, 
whose diameter is about one inch less than the distance between 
the poles of the electro-magnet used, is tacked to the table, and 
enough soft No. 16 iron wire wound around its rim to form a 
coil about three eighths of an inch in diameter. The coil, held 
together by pieces of string tied around it at intervals, is slipped 
off the disk and wound spirally with a narrow strip of brown 
paper. It is then wound evenly with No. 18 "office wire" in 
four equidistant coils, whose ends do not meet by about one inch.f 
The ends of wire in each coil are left from 4 to 5 inches long. 
One or more layers may be wound on each coil, as desired. The 
paper covering between the coils is removed, so as to show the 
construction of the ring. A wheel or circular disk of wood is 
mounted as shown in Fig. 117. The axle is made of a wire nail, 

*For full instructions for making a simple motor, or an electro- 
magnet, without special tools, see Hopkins's " Experimental Science." 

f This is most conveniently performed by winding the office wire 
on to a spool, and then using this spool as a shuttle. If more than 
one layer has been used in the coils, the wheel may need cutting 
down where the coils come. 



234 



APPENDIX G. 



with its ends filed sharp. The upper end bears on a brass screw, 
whose lower end has been filed flat and slightly bored with a 
drill. The screw is inserted in the cross-piece attached to the 
base-board. The lower end of the nail rests in a slight depression 
drilled in the head of a copper rivet. This forms a bearing with 
little friction. The wheel may be removed by raising the screw. 
The ring is crowded on to the wheel and secured by pieces of 
string passing around it and through holes near the rim. A 




circle whose diameter is about half that of the wheel, and whose 
centre is the same, is struck off on the wood ; and four holes, a 
little smaller than four wire nails, are bored through the wood at 
points on the circle 90° apart, and corresponding to the ends of 
the coils. The ends of the two adjacent coils, freed from insu- 
lation from the point, where they enter, are drawn down into the 
same hole, tight, and a wire nail driven in as a wedge. The two 
wires and the nail, which form a sufficient contact, are cut off 
even on the under side, and the nail is allowed to project about 
half an inch on the upper side. Proceed in the same way with 
the other coils. The " brushes" are two pieces of No. 16 copper 



CONSTRUCTION OF APPARATUS. 



235 



wire held by wooden uprights, and connected there by means of 
No. 18 wire, with the two binding-posts. These brushes should 
be adjusted so as to press gently against the nails, without rub- 
bing on the wood when the wheel turns. 







This armature is then mounted under the magnet, as near to 
it as possible without touching, and connections made as indi- 
cated. 

This contrivance has all the essential parts of a dynamo or 
motor. On sending through it sufficient current the wheel will 
revolve, the motion being varied by varying the strength of the 
current, and reversed by reversing the current through the mag- 
net or the ring. If used as a dynamo, the current is sent through 
the magnet only, the brushes are connected with a galvanometer, 
and the wheel is rotated by hand. This contrivance is intended 
merely to illustrate the construction of the dynamo and motor, 
and does not develop power. It shows the construction clearly, 
which a regular motor does not.* 

* In the form used in the author's laboratory the wheel was made 
of the cover of a round salt-box, the ring of 7 cents' worth of iron 
wire, and the magnet was that referred to on page 216, note 22. 
The Edison current was used. 



APPENDIX C. 



Contact Keys.— These may be constructed of sheet-brass about 
4 x i inches, one end turned up for a handle. A hole is bored 
through the other end. Through it is passed a machine-screw, 
one end of a piece of No. 16 wire is twisted around the screw be- 
tween the brass and the wood, and the screw set firmly in, best 
by a nut on the under side of the base-board. For an open cir- 
cuit key the brass is bent so that its free end is about i inch 
from the base-board. Directly below is placed a brass machine- 
screw with the top filed flat, to which a wire is attached. Both 
wires may be led to binding-posts, or a length of 30 or 40 cm. 
may be left permanently attached. This key stands at an open 
circuit. On depressing the key the contact is completed. The 
circuit may be maintained either open or closed by leaving the 
screw so loose that the strip may be rotated, bending the strip 
slightly down, and pushing the end of the strip off and on on the 
machine-screw. 



Sulphate-of-copper Cell. (See Fig. 118.)— The containing ves- 
sel is made by cutting off the upper portion of a flat-bottomed 
bottle whose diameter is an inch or so greater than that of the 
porous cup. The zinc-plate Z is cut out of sheet-zinc, a projecting 
strip being left, and rolled around the porous cup into the form 
of a cylinder, the projecting strip being bent over and having the 
leading-wire attached to it. For the copper plate C one or two 
of the copper strips used in Exercise I can be used. The porous 
cup is filled with a saturated solution of copper sulphate, and the 
zinc plate is immersed in the solution of sulphate of zinc. 



CONSTRUCTION OF APPARATUS. 237 



MENSURATION. 

Measuring Vessels. — Substitutes for burettes, measuring cyl- 
inders, etc., may be constructed as follows : A tube is corked at 
one end and some mercury poured into it. Air-bubbles are care- 
fully removed by means of a feather and wire, as in the experi- 
ment on Boyle's Law. The tube is set upright and the height 
of the mercury-column carefully measured. The mercury is 
weighed, and its weight divided by 13.6 equals the volume. 
Several determinations are made, using various quantities of 
mercury, and the volume in each case when divided by the height 
of the mercury-column gives the cross-section in sq. cm., and 

— — = length on the tube corresponding to 1 cu. cm. 

The simplest way is to attach the tube firmly to a meter-stick, 
and prepare a table, giving the readings on the meter-stick cor- 
responding to the various volumes desired. Or, a scale-reading 
directly in cu. cm. may be ruled on paper, glued on the back of 
the tube, face to the glass. When dry, the back may be well 
shellacked to prevent injury from water. The mercury used 
should be clean and dry. The graduation may be performed 
with water, but mercury is much more desirable, because any 
errors in weighing only produce one-thirteenth the error in the 
volume. Graduates accurate enough for the purposes of this book 
can be obtained by weighing the mercury to a Centigram. The 
chief errors arise from the uneven bore of the tube, and from fail- 
ure to measure accurately the height of the mercury-column. 
This method may be used in calibrating the short arm of the tube 
used for Boyle's Law, and also in graduating flat-bottomed chem- 
ical flasks. 

In Exercise 3 a substitute for the burette may be constructed 
as follows, provided one good burette can be obtained : A piece 
of glass tubing of 8 or 10 mm. internal diameter and about 60 
cm. long is provided at its lower end with a cork through which 
passes a glass tube. This connects at its lower end with a piece 
of rubber tubing provided with a glass ball, as described on page 
73. The whole is firmly lashed to the edge of a meter-stick. A 
little water is poured into the tube, the reading of its level noted 
on the scale, a measured volume of water run in from a burette, 
and the reading of its level again noted. The difference in the 



238 



APPENDIX C. 



scale-readings gives the height occupied in the tube by the known 
volume of water, and the distance on the scale corresponding to 
1 cu. cm. can be readily calculated. Several determinations 
should be made, the average volume taken and marked on a card 
attached to the apparatus. When used, the scale-readings are 
taken before and after running water out of the burette, and the 
difference in the readings divided by the distance on the scale 
corresponding to 1 cu. cm. gives the volume. The preparation of 
such an instrument might be well given as a modification of 
Exercise 4. Increased accuracy in reading can be obtained by 
some such device as that described on page 1&5. 

Scales.— A cheap and useful form are brass hand-scales with a 
6-inch beam. They are sensitive to about .01 grm., and may be 

mounted on a five-pound 
starch-box, as shown in 
Fig. 119, the frame being 
of such height that the 
pans hang about half an 
inch above the upper sur- 
face of the cover. This 
frame is constructed of 
hard pine 2x2 in. The 
scales may be suspended 
from the cross-piece witli 
a screw-eye, or, if there 
is a tendency to turn 
while weighing, a block of 
wood, as A in Fig. 120, 
provided with a slot to 
FlG - 119 - receive the top of the 

scale-support B, which is held by the pin P, may be substituted. 
For suspension weighing, the cover is pulled out and laid cross- 
wise as a support for the weight-pan, as indicated by the dotted 
lines in Fig. 119. 

A body too large for the pan may be conveniently weighed 
by suspension. For specific-gravity work a tumbler of liquid 
may be placed as indicated by the dotted lines in the figure. For 
better observation in this case part of the side of the box may 
be removed. 




CONSTRUCTION OF APPARATUS. 



239 



Oi'oss Piece. 



Another good form, made to order for the author's laboratory,* 
is shown in Fig. 62. The beam is 
supported upon a sharp edge by a 
brass post. The lower end of the 
post is set into the side of a 
starch-box. Either form is fitted 
for suspension by piercing a hole 
through the centre of each pan. 
In the second form a half -inch 
hole is also bored through the 
wood directly below the left-hand 
pan. This form is a little more 
expensive and more convenient 
than the first. The capacity of 
both forms is from 200 to 250 grm., and their sensitiveness is 
nearly alike. 

Substitute Balances. — Balances may be constructed with a 
wooden beam of tough wood and a wooden post attached to a 
suitable base-board. The pans, of tin (spice-box covers will an- 
swer) or stiff card-board, may be suspended by fine wire or trout- 
line. The beam should have some form of knife-edge bearing. 
One device is indicated in Fig. 121. The post P is provided 




Fig. 120. 




with a slot in its upper end about £ inch wider than the beam, 
and deep enough to permit the beam to move freely in a vertical 

* By Ritchie. 



240 



APPENDIX C. 



plane. The projecting ends on each side of the slot are cut in the 
form of a flat " V," with the angle slightly rounded. Pieces of 
sheet-brass are fitted to these notches and fastened in place. In 
the beam is iuserted transversely a knife-edge, K, made of a piece 
of sheet-brass, whose lower edge has been filed sharp where it will 
bear on the sheet-support. Care must be used in weighing that 




the beam does not rub against the sides of the slot. Increased 
delicacy could be attained by projecting beyond the support one 
end of the knife-edge and attaching to it a long pointer reading 
on a scale upon the lower part of the post. In using these scales 
it would probably be best to weigh by substitution, except when 
ratios only are required. 




A form of " Post-office" balances is shown in Fig. 122. The 
beam A is mounted on the post P, and carries a sliding- weight 
W. The play of the beam is limited by the stops 88. The scale 
on the beam is spaced off by finding, by trial with various 



CONSTRUCTION OF APPARATUS. 241 

weights, the average space corresponding to the unit of weight 
used. These spaces with subdivisions are then laid off on the 
beam. This device, mounted on a box, would be very good for 
specific-gravity work. The capacity coiild be varied by using sev- 
eral weights which were multiples, etc. A contrivance for deter- 
mining small weights is shown in Fig. 123. A block of wood, B, 
is attached to a base-board. A piece of glass rod, G, is drawn 
out at one end and fastened to B. The end carries a light scale- 
pan, and the deflections caused by various weights may be read 
on the scale 8. The deflections caused by known weights are 
found by trial, and the scale spaced off accordingly. This instru- 
ment may be made very sensitive, though its capacity is limited, 
by drawing the rod out quite long and fine. Within its limits it 
is quite accurate. 

Weights, — The weights referred to in this book are sets of 
20 grm. to 0.01 centigram in a box. These are supplemented 
by* weights of 50, 100, and 200 grm., made of lead by aid of a sen- 
sitive balance and a large set of weights. For other purposes, 
elasticity, etc., weights of 500 and 1000 grm. were also constructed 
of lead, by the method given below. Provided one set of 
weights and a fairly sensitive balance* are available, sets of 
weights maybe readily made, those of 5 grm. and over of sheet- 
lead, 1 to 5 grm. of sheet-brass or even sheet-iron, and the deci- 
gram weights of thin sheet-brass or wire. For the centigram 
weights wire of iron or copper, or better, sheet-aluminum, may be 
used.t The most convenient method for sheet-metal consists in 
weighing several rectangular pieces of known area, and thus 
determining approximately the average weight per sq. cm. The 
area to give the required weight is computed, and a piece a little 
in excess of this is cut off, transferred to the balance, and care- 
fully worked down by scissors and file to the correct weight. If 
it is to receive a distinguishing mark, apply this before obtaining 
the exact weight. At the last, great care must be used not to 
cut off too much at once. The method for wire is the same, the 
length per grm. being obtained, and calculated lengths for the 

* Home-made will do. The " glass-rod " form will do well for 
the smaller decimals. 

f This can be obtained in sheet or wire of dealers in chemical sup- 
plies, and, owing to its lightness, weights of small denomination are 
of some size. 



242 APPENDIX a 

desired weight being measured from that. When one approxi- 
mate weight is obtained, it may be used as a pattern for others of 
the same denomination. For more on this subject see Picker- 
ing's " Physical Manipulations, page 49." 

DENSITY AND SPECIFIC GRAVITY. 
Specific-gravity Bottles. — A light salt-mouthed bottle is 
used, holding about 100 cu. cm., and provided with a ground- 
glass stopper. Such a bottle weighs about 100 grams, and is 
marked, by means of diamond ink, with the words "Specific 
Gravity." A number is placed upon the bottle and also upon 
the stopper. This prevents the use of the bottles for other pur- 
poses and the interchanging of the stoppers. Somewhat less 
accurate results could be obtained by the use of small medicine- 
bottles, the bottle, being filled in each case to the level of a ring 
scratched around its neck with a file. 

Apparatus for Liquid Pressure. (See Fig. 63.) — The support 
for the gauge bulb is a block of wood, E y 4 x 5£ in., out of which 
is cut a rectangular opening \ in. wider than the bulb, and 3£ in. 
deep. Across the bottom of the opening so formed is stretched 
a wire held by two tacks. To this wire the gauge is attached at 
two opposite points by pieces of wire, which are passed around 
the flange, twisted together, then around the wire, and the ends 
twisted and cut off. The meter-stick is attached to the block, 
with its lower end even with the wire. The rubber tube should 
be sufficiently long to permit the free movement of the gauge. 
The tube is connected at its outer end to a piece of small glass 
tubing 6 in. long, which is tied to a meter-stick and which 
carries a globule of mercury as an index. Several pieces of rub- 
yt ber tubing may be connected by short pieces 
'of glass tubing, but all joints should be well 
wired. The vessel must be large enough to ad- 
l mit of the gauge being immersed to the depth 
) of 6 or 7 inches. An ordinary water-pail is 
'just the thing. The gauge is constructed as 
follows (Fig. 124) : The tube of a "thistle- 
tube " is cut off about \ in. below the bulb. 
Over the mouth of this is drawn, not very 
Fig. 124. tightly, a piece of thin sheet-rubber, which 

is held in position by winding a fine wire around the flange, 




CONSTRUCTION OF APPARATUS. 



243 



The rubber extending beyond the wire is then turned up and 
wired again, just above the first wiring. This usually gives a 
water-proof joint. The superfluous rubber is then cut off. 

Apparatus for Specific Gravity by Balancing. — The simplest 
form of apparatus consists of two glass tubes, about 1 yard long 
and | or f of an inch internal 
diameter, connected by a piece of 
rubber tubing about 10 inches 
long, the joints being wired and 
the whole held in a vertical posi- 
tion by clamps, or on a support. 
The two tubes may advanta- 
geously differ considerably in 
size, as illustrated in Fig. 125, 
where the larger is about f in. 
internal diameter. Its lower end 
carries a perforated cork, pierced 
by a smaller glass tube which 
may either connect with a rubber 
tube, or be bent twice so as to 
form the other upright arm. 
This form needs no funnel. The 
ends of the large tube should be ' 
rounded in the flame before in FlG - 125 - 

serting the cork, which it is well to soak in paraffine. 

Apparatus for Atmospheric Pressure. — The barometer-tube is 
3 ft. long. The device for removing air-bubbles is a feather 
about 2 in. long, cut down to ^ in. in width, fastened firmly by 
thread to the end of a straight, stiff iron wire 3£ ft. long. 

Apparatus for Specific Gravity by Barometric Columns. 
(See Fig. 67.) — A wide-mouthed bottle is fitted with a cork carry- 
ing three tubes, the two longer being about 2 ft. long. The 
third is bent at right angles a short distance below the cork, and 
has attached to it 6 or 8 in. of rubber tubing, which termi- 
nates in a mouth-piece formed from glass tubing 3 or 4 in. long. 
There is also provided a plug of glass rod with which to replace 
the mouth-piece when the tube has to be closed. In order that 
the bottle may be air-tight, the cork with the three tubes inserted 
is immersed for some moments in melted wax. It is then quickly 
removed from the wax, the tubes cleared by blowing through 
them, and the cork crowded into the bottle as tightly as possible, 




244 APPENDIX C. 



HEAT. 

Apparatus for Testing Thermometers.— A piece of large glass 
tubing about 1 ft. long is supported vertically. In the upper 
end is a cork with two holes, one for the thermometer and one 
for the steam-pipe. In the lower end is a cork perforated for 
the escape of the steam. 

Apparatus for the Latent Heat of Steam. (See Fig. 75.) — D 
is a glass bottle of 2 to 4 1. capacity with the bottom cut off, or 
a tin cylinder with a hole in the bottom fitted to carry a cork. 
Make the condensing coil by bending four or five feet of the com- 
mon size of glass tubing into a spiral, with turns about 1 in. apart. 
The diameter should be such that when placed in D there will be 
about an inch between the tubing and the sides of the vessel ; 
the height of the coiled portion of the tubing should be about 
three fourths that of D. The curved form required may be ob- 
tained by bending the tube a few degrees at very frequent inter- 
vals. Sharp bends weaken the apparatus. Pass the lower end 
of the tubing through the cork inserted in the bottom of I), and 
cut it off an inch below. The whole arrangement should be sup- 
ported at such a height that a beaker may be placed beneath. 
The upper part is supported by string or wire. The steam-pipe 
is in three pieces, united by rubber "connections. 1 ' Make the 
steam-trap of 3-in. tubing, the entrance tube passing just through 
the cork, the exit projecting in about an inch. Wind woollen 
cloth or rags tightly around steam-pipe, and trap to within $ in. 
of the level to which D is to be filled with water. Secure the 
wrapping by cotton strings. Arrange the covering so that the 
pipe may be easily disconnected at H. The weight of D with 
cork and coil may be determined, and the value marked on the 
apparatus. 

Apparatus for the Expansion of Gas.— I. (See Fig. 79.) Ves- 
sel B and support as in the apparatus for latent heat. A is a round- 
bottomed chemical flask of 250 to 300 cu. cm. capacity, with the 
neck drawn down to the size of the tube DC. A good substi- 
tute is a glass reagent bottle, with a paraffined cork perforated for 
DC. The tube, about 3 ft, long, is in two pieces, the connector 
being 3 or 4 in. from the bend. It projects about 2 in. above 
the cork in the bottom of B, and communicates witli A by a rub- 
ber connector, or, if a bottle be used, by passing through the 



CONSTRUCTION OF APPARATUS. 245 

cork. Fill A with dry air * (or any desired gas), and attach it to 
the end of DC. If J. is a bottle, the tube must make an air- 
tight joint with the cork ; if a flask, the joints of the connector 
must be wired. Disconnect DC at D and draw a globule of mer- 
cury into the long part of the tube so as to form an index about 
I in. long. Fill B with ice-water, let it stand 5 min., then, by 
gently tipping the tube, bring the index about 4 in. from one end, 
and attach this end to the connector D. If the gas continues to 
contract (as shown by the movement of the index), disconnect, 
move the index back, and connect again. Finally, the index 
should remain at rest a few inches from D. Support the meter- 
stick E on two blocks for ease in adjustment, lay DC upon it, 
and hold them together by rubber bands. 

II. (See Fig. 80.) The jacket is a large glass or tin tube about 
12 in. long, fastened to a base-board by strips of leather. A 
piece of small glass tubing is cut off, about 18 in. long. One 
end is melted so as to nearly close it ; then it is warmed, and air 
as dry as possible drawn through it for a few minutes so as to 
expel any moisture. A globule of mercury is then drawn into 
the open end so as to form a column about 0. 5 cm. long. This 
index is slid along the tube till about 7 in. from the partially 
closed end, which is then melted completely together, thus im- 
prisoning a volume of air between the index and the closed end 
of the tube. The other arrangements are similar to those of 
Exercise 9. 

Apparatus for the Expansion of a Liquid. — Test-tube with 
perforated cork, carrying a small-sized glass tube about 18 in. 
long. If the test-tube used is so long that it cannot be completely 
covered with the ice-water, a portion of the top may be cut off 
and the edges rounded in the flame. The length on the tube, 

* Arrange a large bottle with a long funnel-tube and a delivery- 
tube, so that when water is poured into the funnel air is driven out 
through the delivery-tube. Arrange two or three wash-bottles con- 
taining strong sulphuric acid so that the air will be dried by the acid 
as it is driven from the bottle. From the last wash-bottle lead a 
tube inside the vessel to be used for A. By pouring water into the 
bottle the vessel may be filled with dry air. It is then connected 
with the apparatus, the opening being kept closed as much as pos- 
sible during the operation. For any other gas substitute a genera- 
tor for the air-bottle. 



246 APPENDIX C. 

corresponding to 1 en. cm., is determined as explained in Exer- 
cise 4, Mensuration. The glass tubing is generally of very uni- 
form bore, and the average value as determined by two or three 
trials on one piece, would prebably be sufficiently accurate for all. 
If desired, the determination of this value might be made a part 
of the exercise. The specific gravity of the alcohol at the average 
temperature of the room is determined and marked on the bottle. 
A small flask may be used instead of a test-tube. 

Apparatus for the Expansion of a Solid.— Second Method. 
(See Fig. 78.) The rod R is round, of brass, about 24 in. long and 
I in. in diameter. The jacket is tin pipe or glass tubing, about f 
in. internal diameter and i in. shorter than the rod. The ends 
are closed by double-perforated corks carrying the rod and the 
steam-tubes. One end of the rod screws into a brass plate B, 
which is screwed to the block A. The other end is in line with 
the brass rod D, which has a thread, about 40 to the inch, cut on 
its inner end for about 1 in. This screw works in a brass plate 
E, fastened to the block F. The rod I) passes through a hole 
bored ini'', in which it can just turn, and comes out in the centre 
of the clock-dial (r, which is attached to the other side. It carries 
a pointer, H. The end of the jacket nearest F is held firmly by 
the support C. The corks are cut thin, and the steam-tubes are 
sunk into the cork and the edge of the jacket, as shown, the 
cork coming close against B. At the other end the rod is level 
with the outer edge of the cork. In order to show contact be- 
tween D and the end of the rod, connections are made so that 
when D touches the rod an electric circuit is completed. The 
author uses the Edison current through a 16 c. p. lamp. A tele- 
graph-sounder, galvanometer, electric bell, etc., would answer 
equally well. 

Apparatus for the Expansion of a Solid. — First Method. 
(See Fig. 77.) The rod C is of brass, 24 in. long, £ in. diameter. 
Steam-jacket and connections as in Fig. 78, just described, with 
the addition of a short piece of tin tubing set into the middle of 
the jacket, its upper end closed by a cork perforated to carry a 
thermometer. The base B is a board about 30x6 in., thick 
enough to prevent warping. To this a heavy rectangular block 
of wood, D, is firmly attached as shown. The rod passes through 
the corks, and projects about \ in. from each end of the jacket. 
One end is firmly set into a hole \ in. deep, bored in 2), at such 



CONSTRUCTION OF APPARATUS. 247 

a height above the base-board as to allow the rod and jacket to 
slightly incline towards the other end. The pointer /' consists 
of a piece of square brass rod. Its lower end is pivoted in a 
mortise cut in a block of wood, g, which is firmly fastened to the 
base-board. A little above, it is also attached by a pivot to the 
end of the rod at c, thus forming a second-class lever. To the 
upper end of this rod a fine needle is attached by whipping it on 
with waxed thread and then covering the whipping with shellac. 
A millimeter-scale, S, is attached to an upright rising from the 
side of the base-board and steadied if necessary by two wire 
guys, y, y. The pointer should magnify at least twenty times. 
Through holes in the corks at the ends of the steam-jacket are 
passed glass tubes, i, i. The tube at the higher end of the jacket 
is connected by rubber tubing with a flask, F, holding about .5 
litres, used to furnish steam. One flask will serve for several 
pieces of apparatus. 

DYNAMICS. 

Apparatus for Exercise 1. — Set a strong screw-eye firmly 
into the ceiling, or other suitable support, at least 6 ft. above the 
table — the farther above it the better. From this suspend by a 
strong iron wire a 10 or 12 lb. weight, or a box (cigar, starch, 
etc.) loaded to about that weight. Care must be used that the 
wire and eye are of sufficient strength. Two or three feet of 
common cotton string are attached to the weight. 

Friction Apparatus. — The board is that used in the inclined 
plane (Fig. 89). The blocks may be sawed from hard-pine floor- 
board. Instead of an 8-oz. balance a rubber strip may be used. 
A light strip of wood has a scale on its lower half.* A strip of 
rubber about 18 in. long and J x £ in. is fastened to the upper end, 
as in the apparatus for elasticity (Fig. 95). One or two marks on 
the strip serve as references. A rod attached to the lower end of 
the strip, as in Fig. 95, holds the connecting cord. 

Apparatus for Composition of Angular Forces. — Near one 
edge of the table drive two nails about 2^. ft. apart ; hook over 
these the rings of two of the balance and connect them by a piece 
of cord of such length that when gently pulled at the centre the 

* This may be a centimeter scale marked on the wood, or the ap- 
paratus may be graduated in grams by testing with weights. 



248 APPENDIX a 

balances do not lie in a straight line. Take a second piece of 
string, about 2 ft. long, and tie its centre around the first piece of 
string so that it will slide upon it, but the knot will not slip. To 
the ends of this piece of string attach two other balances. 

Apparatus for Parallel Forces. (See Fig. 88. ) — A 25-lb. balance 
is suspended from the ceiling, or some other support, by an iron 
wire. A hole is bored through a meter-stick at the 50 cm. mark, 
and the meter-stick is suspended from the hook of the balance by a 
loop of strong cord passing through the hole. Two pieces of cord 
about 6 inches long, having loops at their upper ends to slide on 
the stick, are attached to the rings of two 25-lb. balances. The 
meter-stick may be mounted in some such way as that in Exercise 
12, Dynamics. 

The Inclined Plane. (See Fig. 89.)— Two pieces of matched hard 
pine floor-board may be used to form a board 7 in. wide ; they 
may be held together by two cleats on the under side. The 
length is about 6 ft., and the boards are planed. To prevent 
slipping, the lower end may rest against a couple of nails or a 
cleat fastened to the table. The general form of support is indi- 
cated in the figure. In another form, which is easily constructed, 
a piece of hard-pine floor-board about 2£ ft. long is nailed to 
to each end of a starch-box weighted with stones or sand. The 
tops of the uprights are connected by a cross-piece nailed on, and 
several holes are bored in opposite pairs in each upright to receive 
the supporting rod. 

A cheap form of roller-skate, in which the axles are rigid 
and do not turn, and the wheels as far apart as possible, 
makes a good carriage.* The straps are removed, the axles 
oiled, and to one end is attached a screw-eye, to which is 
fastened a piece of fish-line about 12 in. long, with a loop at the 
end. The straps from these skates can be used to attach glass 
tubing to boards. If no skate can be obtained, almost any small 
carriage can be used — a tin cart for instance, provided the fric- 
tion is not very great and the wheels run smoothly. As the fric- 
tion is to be corrected for, the amount, within reasonable limits, 
is not important, provided it is constant. Another substitute 



* The wheels on these skates are often set so that the skate tends 
to run in a curve, and they may need adjusting before they are used 
for the first time. 



CONSTRUCTION OF APPARATUS. 249 

might be a piece of board, or a box, about 4x6 inches, mounted 
on easy-running casters. The total weight of the carriage when 
loaded should be about 15 lbs. If a skate be used, a cigar or 
chalk box, filled with pieces of iron, lead, etc., may be tied on to 
it, or fastened by screws. In loading the carriage care must be 
used to get the centre of gravity as low and as near the centre as 
possible, so that the arrangement will not readily capsize if acci- 
dentally pulled sideways. This experiment calls for two students. 
It could be modified for one student by leading the cord over a 
pulley at the upper end of the board and attaching a scale-pan of 
known weight, the force required being measured by weights 
placed in the scale-pan. In this case the carriage, etc., need not 
weigh over 4 or 5 lbs. For Part II a piece of hard pine 1 in. 
square and 8 in. long, having a hole bored in each end, is screwed 
crosswise to the front end of the skate. A similar piece has at 
its centre a screw-eye or loop of string to hold the balance. The 
two are connected by pieces of strong cord about 4 ft. long. 

Collision Apparatus. — First Method. (See Fig. 92.) The base- 
board is about 3 ft. long and 5 or 6 in. wide. Fasten a meter- 
stick on edge in the centre of the board parallel to its length. 
At diametrically opposite points in each ball drill holes 1 or 2 
mm. in diameter and 2 or 3 mm. deep. Prepare wooden plugs 
which fit tightly in the holes, projecting 2 or 3 mm. beyond them. 
Place the ends of the suspending cords or wires in these holes 
and force the plugs firmly in. The balls may be readily detached 
by withdrawing the plugs. Suspend the balls at the point of a 
V formed by the two wires, arranged, as shown in the figure, so 
that the balls swing freely in one vertical plane. This may be 
done by attaching to the ends of a board about 1x2 ft. two 
screw-eyes, and passing the wire from the ball through one eye 
across the board through the other eye, and back to the ball. 
The board is fastened to the ceiling. The second ball is sus- 
pended like the first, the distances between the screw-eyes being 
so arranged that when both balls hang at rest they just touch, 
and their centres are in the same line, parallel to and just above 
the meter-stick. The two electro-magnets are supported above 
the meter-stick, so that they may be moved either vertically or 
horizontally in the plane in which the balls swing. Find by 
trial the point on the balls which touches the ends of the mag- 
nets. At each of these points drill a small hole, plug it with 



250 APPENDIX C. 

wood, and drive a small iron tack into the wooden plug. If the 
magnets are of sufficient strength the balls can be held in any 
position desired, and released by breaking the circuit. By plac- 
ing both magnets in series, the balls may be released simulta- 
neously. Have four rectangular blocks of wood with two 
upright cards tacked on them on opposite sides. Place these 
blocks beside the meter-stick just clear of the balls, and move 
them along until on sighting across their sides the line of sight 
strikes the centre of the ball. The number on the meter-stick 
struck by the line of sight is the reading for the ball. It saves 
time to mark the weights of the balls on them. The author uses 
the magnets out of old telephone bells, and the Edison current 
through a 16 c. p. lamp. With these coils and this current there 
is some danger of overheating if the circuit is kept closed too 
long at a time. The electro-magnets may be supported on a 
block of wood which slides on the meter-stick, and carries an 
upright rod thrust through a large cork, into which is also thrust 
one of the projecting ends of the magnet. The cork may be 
slipped up and down the rod, and the block wedged in any posi- 
tion on the meter-stick. The most convenient support for the 
magnets, however, is a wooden clamp. The balls weigh about 10 
and 30 grams, respectively. If putty be used, a weighed quantity 
may be spread over one ball, and its weight added to that of the 
ball. 

Second Method. (See Fig. 93.) Remove the handles of two 
pint tin pails and suspend them from the ceiling by wires, whose 
upper ends are about two feet apart. The lower ends hook into 
the holes in the pails where the handles were attached. Make a 
spiral spring about three inches long by twisting spring-brass 
wire tightly around a broomstick. Attach this spring to one of 
the pails at a point 90° from the suspending wires. Arrange the 
distances between the points of suspension, so that when the 
spring is compressed the pails will hang side by side with the 
spring between them. Beneath the pails place two meter-sticks 
end to end, about 1 cm. below, scale side up, and in the plane in 
which the pails swing. 

Apparatus for Boyle's Law. (See Fig. 96.)— The apparatus 
is the usual form, and may be obtained of instrument-makers. 
The tube is made of a piece of " American glass" tubing of about 
8 mm. internal diameter and about 130 cm. long. One end is 



CONSTRUCTION OF APPARATUS. 251 

sealed up in the usual way, care being used to make as square an 
end as possible. The tube is bent into the form shown in the 
figure, the horizontal portion being 5 or 6 cm. long, and the 
short arm about 40 cm. long. The tube is fastened to an upright 
by strips of leather. A meter-stick is attached to the board, 
parallel with the long arm. If the end of the short arm is 
properly sealed, a 40 -cm. scale cut from a meter-stick may be 
attached parallel to the short arm, and the experiment carried 
on in the usual way. The writer prefers, however, to calibrate 
the tube, and hence measure directly, the volume of the gas. A 
convenient method of calibrating is to fill the short arm about 
half full of mercury, invert it, get it as free from air-bubbles as 
possible, and read the position on the 40-cm. scale corresponding 
to the highest point of the meniscus.* The mercury is then 
weighed, and the volume obtained in the usual manner. Two or 
three more determinations are made with larger quantities of 
mercury, carrying the measurements nearer to the bend. From 
these determinations a calibration-card is made out, giving the 
readings on the centimeter scale for each cubic centimeter, and 
the students are shown how to find intermediate values by inter- 
polation. It is not necessary to carry the calibration-card above 
the lower half of the short arm. A scale may be spaced off upon 
card-board, starting from about the middle of the tube and run- 
ning down to the bottom, giving the volumes directly in cubic 
centimeters. 

The arrangement for removing air consists of a stout iron wire, 
to one end of which is fastened by waxed thread a 
strong feather (from a feather-duster), cut down to 
about £ in. in width and 1 in. in length. The wire 
is long enough to reach from the top of the tube to 
the bend, and the upper end is twisted into a ring so 
that when not in use it may be hung on a nail driven 
into the side of the board near the top. The arrange- 
ment for reading consists of a piece of stiff card- 
board tacked on to a piece of a meter-stick about 10 i 
cm. long. The support for this exercise is also used 
for the exercise on Specific Gravity by Balancing. FlG - 
A board about 3 ft. long, 8 in. wide, and | or 1 in. thick, is sup- 

* For correction for meniscus see S. and G., vol. 1, p. 109. 




252 APPENDIX 0. 

ported vertically, either by nailing its lower end on to a weighted 
box, or by fastening it to a base-board about 1 ft. square. The 
Boyle's-law apparatus may be secured to one side and the Speci- 
fic-gravity apparatus to the other. 

Exercises 11 and 12. — The meter stick is supported by means 
of a double hook of heavy wire (as shown in Fig. 126), which 
holds a wire nail passing through a hole bored in the 50-cm. 
mark. The spring may be constructed of spring-brass wire 
wound around a broomstick. 

Apparatus for Elasticity of a Solid. (See Fig. 96.)— The block 
A is screwed to some firm upright, either the side of the room or 
the upright used for Boyle's Law apparatus. 96 cm. below it 
attach the second block in the same manner. The meter-stick is 
secured to these two blocks as shown. The block B is secured to 
the block A with two long wood-screws, not shown in the figure. 
The reading-card C may be made by tacking a card to a 10-cm. 
scale or similar piece of wood, and is held in position by elastic 
bands, BR, slipped onto the meter-stick before it was attached to 
the blocks. One end of* each rubber strip is turned up around a 
piece of lead-pencil or penholder about 2 in. long, D in diagram, 
and is secured by paper-fasteners or rubber cement. The rubber 
should not be stretched around D so tightly as to prevent the 
easy withdrawal of D if one scale-pan is to be used for both strips. 
The scale-pan may be a piece of cigar-box wood of sufficient 
size (say 4x4 in.) to hang clear of the upright when the strip 
is attached to A. It is suspended from D by light wire. To at- 
tach the strip, loosen the screws holding B, pass the end of the 
strip up between B and A, so that about 1 cm. projects above, 
and tighten the screws again. Find by trial a point on the strip 
corresponding to a length of about 90 cm. when the greatest 
weight that is to be used is in the scale-pan. Mark this point 
with ink (it may be well to letter it b) ; half-way between this 
point and the lower side of B mark a second point, a. Prepare 
tlie second strip in the same way. One scale-pan can be used for 
both, or they may be provided with separate pans. 

LIGHT. 

Apparatus for Focal Length. (See Fig. 99.)— The meter-stick 
is secured to a suitable base-board by wire nails or screws passing 



CONSTRUCTION OF APPARATUS. 253 

through holes bored in the meter-stick, the heads being counter- 
sunk. This does not injure the meter-stick for other use. The 
blocks are about 2x2x3 inches, grooved to slide on the meter- 
stick with a little friction, the bottom of the block resting upon 
the base-board. The screen 8 is of cigar-box wood, about 5x6 
inches, covered on one side with card-board or white paper, and 
is attached to the right-hand end of the block. When the block 
is placed upon the meter-stick the screen should be at right- 
angles to the meter-stick and perpendicular to the base-board. 
The same precautions should be used for the other uprights. 
Another piece of cigar-box wood similarly arranged is fitted to 
hold the lens. A spectacle lens of about 6 inches focal length 
answers the purpose. The chimney is supported on three corks, 
which may be glued to the block and be grooved on the upper 
surfaces to receive the edges of the chimney. To use as a photo- 
meter (See Fig. 100), prepare a support similar to that for the 
lens, cutting an opening in it about 2x2 inches. Over this 
opening fasten a piece of unsized paper (that entirely free from 
gloss) with a paraffine spot about 1 in. in diameter in the centre. 
To make paraffine spot, cut in a piece of stiff paper a circular hole 
about 1 inch in diameter, lay this paper upon the unsized paper, 
rub the portion exposed with the end of a paraffine candle, then 
warm the paper (with a hot iron or by other means) enough to 
melt the paraffine. The block C might be provided with a strip 
of cigar-box wood fastened at right angles to the length of the 
meter-stick so as to carry more candles in line. 

For Ex. 3 the instrument is provided with a screen about 5x5 
inches, mounted as in the other exercise, and having in its centre 
an aperture 1 cm. square. For this exercise the light should be 
as near to a point as possible; hence in front of it should be 
placed a card-board screen provided with an opening about 1 cm. 
square, and held by a clamp or suitable support. Or the light 
may be placed in a small box, open at the top, and having a small 
aperture cut in one side at the level of the flame. In preparing 
the apparatus for use in Exercises 1, 2, and 4, candles should be 
provided of such length that at the beginning of the exercise the 
centres of the flames will be slightly above the horizontal line 
passing through the centre of the lens, the grease spot, or the 
opening. It will save time in correcting for true position to 
make the blocks an even metric length, say 8 cm., and mark this 



254 appendix a 

length upon them. Blocks to carry candles should have a line 
ruled across the top midway between the ends and at right angles 
to the length, to mark the centres of the candles. 

Rumford Photometer. (See Fig. 101.)— The meter-sticks, 
blocks, etc., arranged as above. The angle between the meter- 
sticks should bring the two shadows about half an inch apart. 
The screen, about 5x5 in., attached to the base-board by a block 
2 x 2 x Sin. The rod may be a pencil or pen-holder set vertically 
into a hole in the base-board. Any source of light may be used — 
different-sized candles, small kerosene lamp, incandescent lamp, 
etc. The screen 88' may be of stiff card-board, about lx2i ft. 
The most suitable light for Exercises 1 and 4 is an Edison 16 c. p. 
lamp. In Ex. 1 the image of the filament is very easy to focus, 
and the electric lamps are to be recommended on the score of 
cleanliness. They may be mounted in a single pole cut-out at- 
tached to the apparatus, from which slack connecting wires may 
be led. The plane of the filament should be at right angles to 
the screen. It is well to provide some means of screening the 
eye from the light on L while comparing shadows. The distance 
from the rod to the screen might be measured along the line of 
the meter-sticks and marked on the apparatus. 

SOUND. 

Sonometer. (See Fig. 102.)— Strong fish-line may be used for 
the cord cc. The nails for securing the string should be from 2 to 3 
inches apart. Those having sharp corners should be avoided. The 
wires should be of two different sizes, — say Nos. 28 and 30, spring- 
brass, — and should be secured both to nails and to balance hooks 
by taking a round turn, then twisting the end of the wire around 
the main portion. The triangular blocks may be 1 inch high. 



APPENDIX D. 

NOTES AND BEFEKENCES. 

For the convenience of teachers, and in order to show how to 
connect this course of exercises with the usual class-work, there 
follow detailed references to five text-books, whose full titles and 
publishers are as follows : 

Avery's First Principles of Natural Philosophy. New York, 
Sheldon & Co. 

Avery's Elements of Natural Philosophy. New York, Shel- 
don & Co. 

Gage's Elements of Physics. Boston, Ginn & Co. 

Gage's Introduction to Physical Science. Boston, Ginn & Co. 

Hall and Bergen's Text-look of Physics. New York, Henry 
Holt & Co. 

It is thought that one of these will resemble any book likely to 
be used closely enough to render the making of a parallel series of 
references an easy matter. The numbers refer to sections, unless 
otherwise indicated. 

In order to economize space, all of the notes are given a tele- 
graphic brevity of form. The title of each subject is immediately 
followed by some suggestion of the particular educational ends 
which the succeeding exercises are intended to serve. These 
notes will in some sort account for the order in which the sub- 
jects are placed. 

In the hints to teachers the degree of accuracy which may be 
expected is given approximately. Where the result would vary 
with each pupil, an example drawn from actual work is substi- 
tuted for a numerical statement of the probable percentage of 
error. Occasional reference for the use of the teacher is made to 
the books mentioned at the end of Appendix A. 

255 



256 APPENDIX D. 



MAGNETISM. 



How to plan and conduct an experiment, apply the knowledge 
obtained, take methodical notes, and draw inferences. Study of 
phenomena due to condition ; inductive reasoning. This work 
should be made the basis of considerable class discussion, criti- 
cism of notes, etc. 

Exercise 1. — Show how to tabulate results neatly ; advantages 
of this method of recording results. Rudimentary ideas of work 
and energy might be brought out. 

References. Avery's Principles, 1-35, 47, 283, 284 ; Elements, 
1-9, 13-21, 64, 304, 305. Gage's Introduction, 1-4, 11, 167 : Ele- 
ments, 1, 2, 12, 91, 188 (paragraph 1). Hall and Bergen, 1-4, 26. 

Exercise 2. — In Fig. 2 the magnet should be represented as 
horizontal. This arrangement is preferable to the compass, 
because no new apparatus is introduced. 

References. Avery's Principles, 285, 288 ; Elements, 310, 
317 ; Gage's Elements, 197. 

Exercise 3. — References. Avery's Principles. 286 ; Ele- 
ments, 306. Gage' 's Introduction, 165, 166; Elements, lsii. is;. 
Hall and Bergen, 290-292. 

Exercise 4. — Try effect of direction of stroke. A No. 15 
needle is good. Iron dust may be used for Exp. 6. Can pupils 
explain results of Ex. 1 from the results of this Exercise ? 

References. Avery's Principles, 280-282, 287, 291-293 ; Ele- 
ments, 302, 303, 307, 311, 320. Gage's Introduction, 168, 169; 
Elements, 185, 194, 196, 198. Hall and Bergen, 286, 288. 

Exercise 6. — Different methods might be given to different 
students, and comparative results subsequently discussed. I >raw 
attention to the fact that the diagrams obtained are sections of 
the field of force. Models of wood might be easily made, show- 
ing the field in three dimensions, using wires for lines. 

References. Avery's Principles, 204, 289, 290, 294-297 ; 
Elements^ 313-319. Gage's Introduction, 173-176; Elements, 
191-193. Hall and Bergen, 287, 289, 293, 295. 

ELECTRICITY. 

In general, these exercises illustrate the conditions under which 
phenomena develop and those affecting the degree of develop- 
ment, elementary physical concepts, use of instruments in inves- 



NOTES AND REFERENCES. 257 

ligations and determination of comparative values, the dia- 
grammic method of recording results, and the method of drawing 
inferences from comparison of a number of values. 

Exercise 1. — Experiment 1 might be performed by the teacher 
before the class. Part of the class might try placing the wire 
over the needle. 

References. Hall and Bergen, 303. 

Exercise 2. — It would be well to leave strips of copper and amal- 
gamated zinc in dilute sulphuric acid on a closed circuit for a day 
or two, to emphasize the diminution of the zinc and permanency 
of the copper. If possible, let the pupils themselves discover 
that the power to deflect the needle only exists while zinc is con- 
sumed. By leaving the conductor over a compass, effects of polari- 
zation might be noted. If various commercial cells are available, 
let the students examine them, and point out how each fulfils the 
conditions observed to be necessary. For pictures of many 
modern cells, see the advertising pages of the Electrical World. 

References. Avery's Principles, 246-249, 254-263 ; Elements, 
373-377, 381-386. Gage's Introduction, 128, 130, 135, 136, 138- 
141 ; Elements, 151-154, 158-166. Hall and Bergen, 305-307, 310. 

Exercise 3.— In case of limited equipment, two or three large 
cells with long conducting wires might be used for a half-section, 
and this exercise alternated with Exercise 4. In this connection 
the method of recording results by diagrams, with arrows to indi- 
cate motion, might be suggested. Results may be recorded very 
rapidly if a set of diagrams without the arrows have been previ- 
ously placed in the note-book. Reading by reversal is the best 
method. A reverser is to be recommended as a convenience ; 
but, since it is not absolutely required, it is not referred to in the 
instructions, nor does it appear in the diagrams, although given 
in the lists of apparatus in Appendix B. Should it be used, the 
instructor should show the class the manner of connecting it and 
its action. (See Appendix C.) It might be permanently attached 
to the galvanometer, the two free posts being considered as the gal- 
vanometer-posts, the galvanometer sign in diagrams covering both. 

References. Avery's Principles, 277 ; Elements, 390, 391. 
Gage's Introduction, 131, 132, 149, 150 ; Elements, 156, 157, 
172-175. Hall and Bergen, 313, 314. 

Exercise 4.— The effect of temperature on resistance may 
either be given or be illustrated by experiment, Iron-spiral, 







258 APPENDIX D. 

sensitive galvanometer, burner, etc. If the class have no idea of 
the yard, a yard-stick might be shown to give some idea of the 
lengths of wires used. 

Preferences. Avery's Principles, 216, 220, 270, 271 ; Elements, 

378, 397-402. Gage's Introduction, 143, 144, 152, 191, 192, 197 ; 
Elements, 169, 170, 177, 178, 237, 238, 246. 

Exercise 5. — Fill cells well up to reduce the internal resistance. 
It might be well to explain what is meant by "cross-section," and 
how it is indicated by number. For tables of gauge numbers, 
see Hall and Bergen, p. 372 ; Chute, p. 365. 

References. Avery's Principles, 268, 269, 312, 313 ; Ele- 
ments, 387-389. Gage's Introduction, 142, 159, 187-190 ; Ele- 
ments, 167, 168, 232-236. 

Exercise 6. — Internal resistance should be made high by using 
only enough fluid to immerse the plates to about one third their 
depth. The use of connectors avoids twisting the ends of wires. 
The diagramic sign in Fig. 27 is simplified in Figs. 29, 30, and 31, 
but is essentially the same. Either form is allowable. In con- 
nection with the ohm, a piece of wire about 1 sq. mm. c. s. would 
give an idea of the size of the mercury column. The explanation 
in the instructions is given chiefly with the idea of showing how 
the standard is obtained by attaching specific values to all the 
variables of which resistance is a function. An ohm of some 
conductor might be shown, say about 4 meters No. 28 copper 
wire. For description of B. A. ohm coil see Stewart and Gee, 
vol. ii. p. 161 ; Electrical World, Jan. 10, 1891. Various forms 
of resistance boxes are described in Stewart and Gee, pp. 133, 148, 
158. 

References. Avery's Principles. 250, 264-267 ; Elements, 

379, 380. Gage's Introduction, 153-155, 160-163; Elements, 
177 (paragraph 2), 179, 183. Hall and Bergen, 316, 319. 

Exercises 7, 8A, 8B. — Alternative methods : 7, where no re- 
sistance-boxes are available ; 8A and 8B, where some form can 
be used. For relative resistance iron may be roughly taken as six 
and German silver as twelve times copper under the same condi- 
tions. For tables, see Chute, p. 364 ; Hall and Bergen, p. 374. 
In 8A and 8B, bodies suited to the capacity of the box would be 
required. Lengths of various wires stretched back and forth be- 
tween tacks on a board, lengths on racks for Exercise 7, etc., 
or even the wire coils could be used. Wires wound in coils 



NOTES AND REFERENCES. 259 

would not give very accurate results, owing to inductive effects. 
In 8B, two or three sulphate- of- copper cells in series would give a 
good current to work with. Values could best be checked by 
results obtained by the instructor on the same apparatus. For 
full discussion and description of these methods, see Stewart and 
Gee, vol. ii. pp. 94-97, 105-110. Daniell, p. 591. 

References. Gage's Introduction, 156. 

Exercise 9. — This might be given directly after Exercise 5, or 
explanation of the results of Exercise 6 deferred until E. M. F. 
had been discussed. Dilute sulphuric acid might be used. There 
may be less danger of getting acid on hands or clothes if vessels 
of water are provided in which plates can be rinsed before hand- 
ling. For discussion of electrical units, see Everett, pp. 140-148. 
For standard cells, Electrical World, June 20, 1891. Methods of 
measuring E. M. F., Stewart and Gee, pp. 237-249 ; Kohlrausch, 
pp. 222-225. 

References. Avery's Principles, 218, 219, 251-253, 273, 274 ; 
Elements, 378. Gage's Introduction, 133, 134, 146, 157, 158, 
186 ; Elements, 155, 180-182, 184. Hall and Bergen, 311, 317. 

Exercise 10. — Results of Experiment 1 may be well recorded 
by diagrams and arrows. In Experiment 3, the current strength 
might be changed by using mercury-cups and coils as in Exercise 
6, or the apparatus for Exercise 7. Suggestion : Let pupils de- 
vise some method utilizing apparatus that they have already used. 

References. Avery's Principles, 202, 203, 205, 275, 276, 298- 
300 ; Elements, 392-396. Gage's Introduction, 170, 171, 193-195 ; 
Elements, 171, 188 (paragraph 2)-190, 240-244. 

Exercise 11. — This exercise deals with the fundamental prin- 
ciples of the dynamo and the motor. It may be worked by two 
students, one to watch the galvanometer and the other to handle 
the magnets. If desired, however, it may be worked by the 
teacher and class together. In that case, some sort of an indi- 
cator had better be attached to the galvanometer needle, such as 
that described in App. C. If possible it should be followed by 
instruction on the motor and dynamo, which might be illustrated 
first by a model, as in App. C, and then by a real motor which 
can be taken apart. A talk on the commercial applications of 
dynamic electricity would be interesting. For illustrative cuts, 
see Electrical World, Scientific American, etc. For explanation 
of action of dynamo, see " Shaw" or "Experimental Science." 



260 APPENDIX D. 

References. Axerfs Principles, 206, 278, 303-311, 314, 315; 
Elements, 403-414. Gage's Introduction, 178-185, 196, 198, 199 ; 
Elements, 200-206, 245. 

For practical applications of electricity, see such publications as 
the Electrical World and the Scientific American. The following 
may be of interest : Course of Electrical Reading, Dr. Lewis Bell, 
Electrical World, Aug. 8, 1891 ; Hertze's Experiments, Electrical 
World, July 25, 1891 ; Electrical Units, E. W., Jan. 3, 1891. 

MENSURATION. 

Determination of single values in terms of various standard 
units. Training in the use of measuring instruments. Determi- 
nations requiring simple mathematical work in finding required 
results. Results calculated from experimental data. General 
methods of quantitive work. Errors. Determination of one 
value by several special methods. 

Exercise 1.— Practice in the use of linear scales. Fair values, 
39.45 to 39.30, crosses about 40 cm. apart. As this is the pupil's 
first quantitative work, full tables are given. The less the distance 
between the crosses the greater the error. For accurate deter- 
mination of length, see Stewart and Gee, vol. i. pp. 1-45. 

References. Avery's Principles, App. B ; Elements, 22-30, 
33-36. Gage's Introduction, App. Sect. A ; Elements, App. 
Sect. A. Hall and Bergen, App. 1. 

Exercise 2. — Average of trials should be very near 3.14. 
Examples: 3.14, 3.14, 3.14, 3.15, both methods, two circles. For 
accurate determination of volume, see Stewart and Gee, pp. 104- 
113. Area, pp. 95-104. Calibration, Pickering, pp. 37-39; 
Stewart and Gee, vol. i. 7, 109. Cleaning mercury, Pickering, 
p. 35. 

Exercise 3.— Method B should give results slightly higher than 
A or C, which should give results about alike. The difference 
maybe 0.2 cu. cm. Examples: A 7.5 cu. cm., B 8.0 cu. cm., 
C 7.4 cu. cm. Chief error, careless reading. 

References. Avery's Elements, 31. 

Exercise 4.— In tubes 10-12 mm. diameter, calculated and 
measured results should agree to first decimal place. Two 
methods should agree closely. Examples : .626 sq. cm., .627 
sq. cm., by one student ; .625, .629, by another. For description 



NOTES AND REFERENCES. 261 

of accurate determination of weight, etc., see Stewart and Gee, 
vol i. pp. 61-94. Pickering, pp. 46, 47. 

References. Gage's Introduction, 12, Hall and Bergen, 5, 6. 

Exercise 5. — Practice in the use of balances and scales. Chief 
error in reading spring balance. Bodies weighing 50 to 75 grm. 
best. Examples of results : 28.29 g., 28.3 g., 28.08 g. 

Exercise 6. — Given if needed. For full discussion of errors, 
etc., see Kohlrausch, pp. 1-23 ; Stewart and Gee, vol. i. 
App. A. 

Exercise 7. — An exercise in weighing liquids. For accuracy, a 
correction should be made for the liquid adhering to the sides 
of the vessel from which liquid is poured when the two are mixed. 
Probable error, 0.3 g. 

DENSITY AND SPECIFIC GRAVITY. 

Determination of physical ratios by measurements of two inde- 
pendent values. Special methods based on mathematical use of 
knowledge already obtained. Interpolation of experimental data 
in formula?. Indirect measurements. 

Exercise 1. — Object, to give a clear idea of density and its re- 
lation to specific gravity. For general discussion and accurate 
methods of determining relative density, etc., see Stewart and 
Gee, vol. i. pp. 114-162. 

References. Avery's Principles, 165-167 ; Elements, 241-243. 
Gage's Introduction, 8, 53, 54 ; Elements, 7, 62, 63. Hall and 
Bergen, 47, 48, 52, 53. 

Exercise 2. — The method of determining specific gravity by the 
specific-gravity bottle is given first because this determination 
calls for no indirect measurements, being the direct determina- 
tion of the weights of equal bulks ; hence the principle is more 
easily grasped by the student than the specific-gravity determina- 
tion involving indirect measurements. Probable error, 2 per 
. cent; example : copper-sulphate solution, 1.05 and 1.07, by dif- 
ferent pupils with different apparatus. 

Exercise 3. — A necessary preliminary to the determinations 
following. The student is expected to discover Archimedes 1 princi- 
ple as a fact, the explanation being taken up later in connection 
with the experiment on Liquid Pressure. It is very essential that 
this fact should be thoroughly grasped before taking up the sue- 



262 APPENDIX D. 

ceeding exercises. If the fact that a body loses weight when im- 
mersed in a liquid is not known to all the class, a simple qualita- 
tive experiment will readily show it. It is best to use a body of 
low specific gravity (1.5 to 2), 10 to 20 g. weight. Example : 
Electric-light carbon — loss of weight, 8.03 g. ; wt. of water dis- 
placed, 8.05 g. 

References. Avery's Principles, 162 ; Elements, 237, 238. 
Gage's Introduction, 51, 52 ; Elements, 61. Hall and Bergen, 
50, 51. 

Exercise 4. — Good examples of indirect measurement. Experi- 
ment 1: For best results the body should weigh 30 to 50 grams. 
The best thing for suspension is a piece of the finest copper wire 
obtainable, — say No. 30. It may be well to explain the error due 
to the weight of the wire, and the reasons why it may be neglected. 
Example : Carbon, 1.7, 1.5 ; different pupils with different pieces 
of apparatus and different pieces of carbon. Exp. 2 optional. 
A cork may be used. For accuracy, it is best shellaced or dipped 
in melted paraffine. 

References. Avery's Principles, 168 ; Elements, 244, 247. 
Hall and Bergen, 55. 

Exercise 5. — The fact that liquids exert a pressure on bodies 
immersed in them is usually a matter of common observation ; 
but if necessary, this exercise may be preceded by a qualitative 
one demonstrating the fact. Either one of those given in the 
text-books, or some such experiment as the following, may serve : 

Apparatus. — A lamp-chimney ; sheet-rubber ; glass jar large 
enough to hold chimney. Tie* the rubber over one end of 
the chimney, and thrust it into the water. The bulge of the 
rubber diaphragm will show that a pressure is exerted on the 
bottom. Other modifications will readily suggest themselves. 
Before taking up the laboratory exercise the class might be called 
upon to state the conditions that they suspect would influence 
liquid pressure, the conditions of working, etc. It is best to set 
up the apparatus so that the gauge can be under water over- 
night. Only general results are expected. Before commencing 
the exercise be sure that all the gauges are water-tight, as any 
leakage will make trouble. 

References. Avery's Principles, 39, 146-158, 171-177 ; Ele- 

* See this exercise, App. C. 



NOTES AND REFERENCES. 263 

ments, 215-231, 254-267. Gage's Introduction, 9 (paragraph 2), 
31, 45-48, 37 ; Elements, 43-45, 52-55. Hall and Bergen, 27-30, 
32-38, 65, 66. 

Exercise 6. — Intended not only as a specific-gravity determi- 
nation, but also to impress on the student some of the prominent 
facts of hydrostatics. If desired, the formula a x D = a ' x D' 
could be discovered experimentally, by using liquids of known 
densities, and the explanation subsequently given. This exercise 
also explains the tendency of water to seek its level, etc. , and is 
made the basis of instruction in all these points. The author uses 
both forms of apparatus, but prefers that given in App. C. Ex- 
amples : Kerosene, 0.79, 0.79, 0.80. 

References. Avery's Principles, 160, 161 ; Elements, 232-234. 
Gage's introduction, 49 ; Elements, 56-58. Hall and Bergen, 60. 

Exercise 7. — The chief error lies in reading the volume with 
the test-tube floating in the liquid. If desired, an exercise could 
be introduced here on the determination of specific gravity by 
"flotation," using a rectangular piece of board and measuring 
the depth to which it sank, as compared with the thickness of the 
board. 

Example of results : Weight of tube, 13.5 g. ; wt. of water dis- 
placed, 13.5 g. ; copper sulphate, 13.25 g. 

References. Avery's Principles, 163 ; Elements, 240, 249- 
252. Gage's Introduction, 57; Elements, 60, 61 (paragraph 2), 
64. Hall and Bergen, 58. 

Exercise 8. — Shows how the pressure of the atmosphere may 
be actually measured in units of weight and on given areas, and 
should be preceded by one showing that air has weight. Many 
devices to illustrate this can be obtained of dealers in apparatus,* 
but as they are quite expensive, one of the following may be sub- 
stituted, (a) When an air-pump is available, a bottle holding 
from 1 to 2 litres is provided with a perforated stopper (either of 
rubber or cork which has been boiled in melted wax and inserted 
hot), carrying a rubber tube about 6 in. long, on which is a screw 
clamp. t The rubber tubing should be well wired to the glass. 
Connect the tubing with the air-pump, exhaust as much as possi- 
ble, close the clamp tightly, and counterpoise on the scales. Open 

* James W. Queen & Co. E. S. Ritchie & Sons. 

f This form of clamp is given in E. & A.'s Cat. No. 5968. 



264 APPENDIX D. 

the clamp and admit the air. With a good degree of exhaustion 
the increase in weight is very noticeable. An aspirator might be 
substituted for the air-pump. 

(6) Where no air-pump can be obtained,* a thin glass flask, 
as large as is available, is used instead of the bottle, and 
filled with the perforated stopper, etc. For the clamp a glass 
plug may be substituted. Put some water into the flask and 
boil until the flask is full of steam. Then remove the flame and 
insert the cork, the tube being closed by plug or clamp. Allow 
it to cool, and proceed as above. Having established the fact 
that air has weight, apply the principles of Exercises 5 and 6, 
and so lead up to the principle of the barometer, considering it 
a case of balancing columns, where one column is air. By 
working in this way, familiarize the students with the principles 
of the barometer, and then go on to the exercise, which the 
teacher might prefer to work with the aid of the class, rather 
than to put it directly into their hands, owing to the amount of 
mercury required, and somewhat delicate manipulation. It may 
be well to make sure that the pupils understand that the object 
of completely filling the tube with mercury is simply to expel all 
air. Results probably slightly under theoretical. It might be 
interesting to repeat the experiment with some other liquid, and 
see if pupils can explain the different results. 

References. — Avery's Principles, 178-194 ; Elements, 268-281, 
288-301. Gage's Introduction, 31, 35, 36, 40-44 ; Elements, 
43-49, 51, 59, 60. Hall and Bergen, 39-43, 61, 62, 67-69. 

Exercise 9. — A correction for capillarity might be made. Re- 
sults should closely check those of Exercise 6. Example, copper 
sulphate solution, by Ex. 6, 1.07 ; by Ex. 9, 1.06. 

References. Avery's Elements, 235, 236. Gage's Introduc- 
tion, 29, 30 ; Elements, 34. Hall and Bergen, 60 (paragraph 2). 

For miscellaneous tables of specific gravity, see Chute, p. 361 
363. 

HEAT. 

Graphical method of recording results ; correction for known 
errors ; use of more complicated formulae ; calibration of appa- 
ratus ; more complicated calculations. 

*A simple form of air-pump is described in "Experimental 
Science." 



NOTES AND REFERENCES. 265 

Exercise 1. Before taking up the exercise on Conduction, etc. , 
the ordinary phenomena produced on heating a body are shown 
the class by means of some of the common qualitative experi- 
ments. For convenience, an outline of the apparatus used in 
this course is given here. It would be a matter of judgment with 
the teacher whether to perform them before the class, or give 
them out as Laboratory exercises. 

Change 4 of volume produced by a rise of temperature for solids. 
The apparatus given for Exercise 9, method 1, may be used. It 
is a good plan, however, to remove the steam-jacket and heat the 
rod directly. For liquids, the apparatus for Exercise 10 might 
be used. The liquid used is water or alcohol. If this is to be 
used as a lecture experiment, the liquids had best be colored by 
the addition of black or red ink and a strip of white cardboard 
placed behind the tube. The arrangement is then heated. For 
gases, the same apparatus as above, without the liquid. It is 
supported in an inverted position, the lower end of the tube be- 
ing immersed in a glass cylinder containing liquid. By slightly 
warming the flask, a few bubbles of air will escape, and while the 
air in the flask is cooling to the temperature of the room, a column 
of the liquid will be drawn up into the tube, which will serve 
as an indicator. The warmth of the hand is usually sufficient to 
produce a marked change in the index. These arrangements are 
obviously models of thermometers, and may be used later to illus- 
trate the principle of those instruments. The peculiar behavior 
of water as regards expansion may be illustrated with the same 
apparatus by placing the flask filled with water, as above, for 
some time in a mixture of ice and salt ; upon applying heat, the 
liquid column will first sink and then rise. A similar piece of 
apparatus filled with alcohol might be used at the same time to 
make the contrast more marked. 

References.— Avery's Principles, 358, 361-364, 392-397; Ele- 
ments, 474, 475, 483-491, 537-542. Gage's Introduction, 99-106; 
Elements, 102, 106, 108-113, 116. Hall and Bergen, 134-137, 
189-192. 

Exercise 2. Before taking up this exercise, the class should be 
shown the special form of thermometer used and instructed in 
methods of graduation. The thermometers usually need testing, 
the point being often displaced. In actual use, the correc- 



266 APPENDIX D. 

tion is needed in Exercise 3 and some others. Of course, where 
differences are taken, no correction is needed. 

This Exercise also shows the principle on which thermometers 
are graduated. The apparatus used in Exercise 10 may be gradu- 
ated by using mercury arid noting the distance that the column 
rises when the test-tube is first immersed in ice and then in steam. 
Rise corresponding to 1° F. or 1° C. can then be calculated. 
This would form a good lecture experiment in connection with 
instruction on the graduation of thermometers. For the temper- 
ature of steam at different pressures, see Stewart, p. 11. For 
general discussion of thermometers, ibid. 1-24. 

References. — Avery's Principles, 359, 360 ; Elements, 476-482, 
Gage's Introduction, 107-109 ; Elements, 117-123. Hall and 
Bergen, 138, 139, 142, 143. 

Exercise 3. The effect of temperature on physical form is illus- 
trated by heating in test-tubes such substances as wax, paraffine, 
water, etc. To illustrate the direct change from a solid to a gas, 
a few crystals of iodine may be heated in a dry flask. In connec- 
tion with these experiments, explanations may be given of what 
is meant by the " melting-point, 1 ' "boiling-point," etc. The 
chief object of these experiments is to place the students in pos- 
session of certain facts which form the basis of the subsequent 
exercises, in order that they may bring to the work fair under- 
standing of the principles involved. Vigorous stirring and finely 
broken ice are the main requisites for satisfactory results. A 
good method of breaking ice consists in wrapping it in a stout 
cloth and pounding it against a brick wall. Snow may be used 
in place of the ice, but must be thoroughly mixed with the water 
and not allowed to remain in lumps. If the thermometer rises be- 
fore the ice has entirely melted, it is probably due to an insuffi- 
cient mixture of water and ice, or to the gas having been turned 
on too much. 

References. — Avery's Principles, 369-371, 373 ; Elements, 
53-60, 495, 498-501, 508. Gage's Introduction, 9, 110, 113; 
Elements, 15-17, 131, 361. Hall and Bergen, 167, 168, 175, 
177-184. 

Exercise 4. Probably only general results will be obtained. 
The best vessels to use are beakers holding 15 to 25 cu. cm. If 
different volumes are taken by different students, the effect of 
quantity on the rate of fall in temperature may be observed. A 



NOTES AND REFERENCES. 267 

comparison of the heating and cooling curves might be instruc- 
tive. For law of cooling, see Stewart, pp. 24-27. 

Exercise 5. — For another method, see Journal of Analytical 
Chemistry, vol. 1, Part 1. Paraffine (38-52), lard (33), butter 
(33), wax (65), might be used for the solid; alcohol (79), carbon 
disulphide (48), ether (35), for liquids. For tables of boiling and 
melting points, see Chute, pp. 368, 369. General discussion, 
Stewart, pp. 86-158. 

References.— Avery's Principles, 37-42, 368, 372, 374; Ele- 
ments, 496, 502-507, 510-513. Gage's Introduction, 110, 111, 
113; Elements, 128 (p. 160), 130. Hall and Bergen, 169, 170, 185. 

Exercise 6. This is a preliminary to specific heat, and may 
be used as a specific heat determination. The analogy between 
the relations of specific heat and heat capacity and density and 
specific gravity generally aids in giving a clear idea of what 
specific heat really is. 

References. — Gage's Elements, 139, 140. 

Exercise 7.— "With a glass calorimeter the radiation error is 
very slight. It might be well to make sure that the students un- 
derstand the calculation before making the determination. This 
might be done by giving them imaginary (preferably incorrect) 
data to work up at some time previous to the exercise. TTe use 
cast-iron balls weighing about 130 g., from which we expect from 
.115 to .120. Glass, lead, ivory, etc., are also occasionally used. 
Results are best checked by the work of the instructor or by the 
average results of the class. For tables, see Chute, p. 370. Gen- 
eral discussion, Stewart, pp. 285-303. 

References. Avery's Principles, 376, 387-390 ; Elements, 
514, 531-536. Gage's Introduction, 114 ; Elements, 132, 141- 
143. Hall and Bergen, 160-163. 

Exercise 8. — Results depend largely on care used : 530-545 can 
be obtained if the student is careful. If desired, the weight of 
the calorimeter and coil might be marked on the glass once for 
all, in order to save time. ^Ye obtain our best results with about 
3500 g. of water. The chief error seems to be inaccurate reading 
of the thermometer, and insufficient stirring. In absence of litre 
flasks, the calorimeter could be filled previous to the exercise and 
the temperature brought down to about 10° by ice or snow, or 
glass-stoppered bottles containing known volumes might be used. 
Covering the top of the calorimeter with a piece of card-board, 



268 APPENDIX D. 

having openings for the steam-pipe and paddle, might tend to 
check any loss due to evaporation. — Part II. Calculation : The 
same as for Part I, IF being taken as the water put into the calo- 
rimeter plus one half the condensed steam. General discussion, 
Stewart, pp. 304-311. 

PwEFERENCES. Avery's Principles, 377-385 ; Elements, 515- 
529. Gage's Introduction, 115-118 ; Elements, 132 (paragraph 2) 
-138. Hall and Bergen, 171, 172, 186, 188. 

Exercises 9, 10, and 11. — Alternatives : Exercise 9. Examples : 
Different students with different apparatus. Brass, first method, 
00001800 and 00001669 ; second method, 00001809 and 00001785. 
The ice-water may be dispensed with and the first temperature 
of the rod taken as the temperature of the room. The use of ice- 
water, however, impresses on the mind the fact that the length 
at is that actually used in the determination of the coefficient, 
and gives a fixed value to start from. The apparatus for the 
second method might be used for an additional exercise in Men- 
suration, the student using it as a micrometer-screw to get 
thickness of sheet-iron, sheet-brass, etc. — Exercise 10. Example 
(0° to 24°), .0093 theory, 1°, 001049.— Exercise 11. Might cali- 
brate apparatus previous to exercise. The value of 1 cm. on the 
tube and the volume of vessel A may be marked upon the appa- 
ratus. Fair values, 00365, 00367 ; second method, somewhat less 
accurate. For tables, see Chute, pp. 368, 369. Brass, .00001875. 
General discussion, Stewart, pp. 25-84. 

References. Avery's Principles, 366 ; Elements, 492-494. 
Gage's Elements, 114,' 115, 124-128. Hall and Bergen, 144-151, 
152, 155-159. 

Exercise 12. — Example : Part I. In five minutes, black can 6°, 
bright can 3.5°, rise in temperature. Part II. Black can 18°, 
bright can 16°, fall in temperature, in 15 min. 250 g. of water 
in each can. General discussion, see Stewart, pp. 172-252. 

References. Avery's Principles, 398-404 ; Elements, 545- 
559. Gage's Introduction, 313-316 ; Elements, 357-360. 

Exercise 13. — Warm water is used to save time. About 25°. 
Time might be saved by providing the sugar, etc., in little pow- 
ders containing the required weights. In Part VI a curve 
might be plotted. 

References. Avery's Principles, 23 ; Elements, 41, 42. 
Gage's Introduction, 6, 7, 21 ; Elements, 22-25, :><> 42. 



NOTES AND REFERENCES. 269 

DYNAMICS. 

Working out data by geometry ; investigation of laws requir- 
ing the comparison of a series of measurements of two independ- 
ent variables ; working out formulae. 

Before taking up the first exercise, the ideas of the class about 
forces, their effects, the conditions necessary to develop them, 
and their characteristics, might be brought into definite shape. 
From their work on Magnetism and on Ampere's Law in Elec- 
tricity, they should be familiar with magnetic force and electro- 
magnetic force. From weighing and general experience they 
should know something of the force of gravitation, and their gen- 
eral experience should have made them more or less acquainted 
with other forces. By going over the exercises on Magnetism, 
and that on Ampere's Law, with the aid of their general in- 
formation, all the preliminary ideas required might be brought 
into shape by discussion in the class. 

The main points to be brought out are as follows : That a force 
is anything corresponding to our idea of a push or a pull ; that 
all we can observe when a force is present is motion ; that by 
this motion we recognize the presence of a force ; that two bodies 
(or parts of bodies) are required for the production of a force ; 
that the action is mutual ; that contact is not necessary ; that 
forces are usually named from the conditions under which they 
are developed ; that they vary in strength, direction, and point of 
application. All this can be brought out by questions on the 
experiments cited above. 

Exercise 1. — Maxwell's Matter and Motion, Hall's Elementary 
Ideas, Definitions, and Laws in Dynamics. 

Keferences.— Avery's Principles, 46-57 ; Elements, 38, 64, 70, 
72-78. Gage's Introduction, 10-14, 59-61, 63, 65 (paragraph 2), 
75, 79, 80; Elements, 12, 65-69, 76 (pp. 101, 102). Hall and 
Bergen, 70, 71, 73, 74, 106-111, 114, 115. 

Exercise 2.— The coefficient might be calculated. The aver- 
age results of a number of trials made on different parts of the 
board in each case will probably give the best results for pur- 
poses of comparison. 

Eeferences. Avery's Principles, 142, 143, 409 ; Elements, 
212-214, 65-69, 81. Gage's Introduction, 62 ; Elements, 95, 97. 
Hall and Bergen, 72, 81, 112, 121-124. 



270 APPENDIX D. 

Exercise 3. — The author performs Experiments 1 and 2 before 
the class. Best results when balances are held by nails. That 
pupils may understand the principle upon which Experiment 3 
is conducted, special care must be used that the force which 
holds the point against the combined action of the other two is 
not considered as the resultant itself. The accuracy of the dia- 
grams obtained will depend greatly on the care used in laying off 
the lines, reading the balances, etc. 

References. — Avery's Principles, 133, 135-138 ; Elements, 79, 
80, 82-92, 163, 166, 198-201. Gage's Introduction, 64, 65 (para- 
graph 1); Elements, 70, 71. Hall and Bergen, 75, 77-80, 82. 

Exercise 4.— Three pupils. Ex.: BxBdl04, 57 CxCd 105, 
60. 

This exercise is also made the basis of instruction on the 
centre of gravity, considering the centre of gravity as the point 
of application of the resultant of all the parallel forces which 
together make up the weight of a body. See Lodge's Mechanics, 
p. 114. For an exercise on the determination of the centre of 
gravity by momenta, see Hall and Bergen, p. 121. 

References. Avery's Principles, 65-73, 109-116, 118-131 ; 
Elements, 107-117, 168-197. Gage's Introduction, 66-69, 72-74; 
Elements, 72-76. Hall and Bergen, 83, 84, 86-94, 97-104. 

Exercise 5. — Probable error, 1 ft. lb. The greater the angle 
the less the error seems to be. 

References. Avery's Principles, 92-97, 105-108, 133, 134, 
406-418 ; Elements, 150-155, 164, 165, 202, 203, 561-578. Gage's 
Introduction, 82-85, 89, 94, 95, 119-126 ; Elements, 88-91, 100- 
105, 144-150. Hall and Bergen, 125, 126, 128, 193-198. 

Exercise 6. — It may be well to emphasize the fact that work 
is reckoned by multiplying the force by the distance measured in 
the line of the force ; in this case Dh. Errors about the same as 
in Exercise 5. For full discussion of Thermo-dynamics, see 
Stewart, 77, 312-360. 

References. Avery's Principles, 139-141 ; Elements, 205-211. 

Exercise 7.— Pupils may need help in getting out the formula. 
Example where L : 1/ = 1 : 2, V : V = 1 : 1.34. A curve might be 
plotted. 

References. Avery's Principles, 59-64, 75-82. 84-90, 98-103 ; 
Elements, 98-106, 118-136, 137-149, 156-162. Gage's Intro- 



NOTES AND BEFEBENCES. 271 

duction, 76-78, 81 ; Elements, 18-21, 77-84, 92, 98, 99. Hall 
and Bergen, 113, 117, 129-133. 

Exercise 8. — For preliminary discussion, see Hall and Bergen, 
p. 143. Three students can work well together. The sums 
of momenta after collision are usually a little less than those 
before. The weights of the balls may be determined once for all. 
For greater accuracy, one half the mass of the suspending wires 
should be added. The substitute experiment is somewhat less 
accurate. 

References. Avery's Principles, 54-57, 103 ; Elements, 70-72, 
93-97, 162. Gage's Introduction, 70, 71 ; Elements, 85-87, 93, 
94. Hall and Bergen, 118, 119. 

Exercise 9. — It may be well to caution students against getting 
their faces so close to the balance as to be injured by the flying 
up of the hook when the wire breaks. 

References. Avery's Principles, 32 ; Elements, 48. Gage's 
Introduction, 20 ; Elements, 32. Hall and Bergen, 7, 9, 25. 

Exercise 10. — The stretch will increase as the loads are made 
greater owing to the reduction of cross section. Example : load 
of 50 g., stretch, 0.8 cm. ; load of 550 g., stretch, 10.47 cm. A 
curve might be plotted from the data. For discussion, see 
Stewart and Gee, vol. 1, p. 170. 

References. Avery's Principles, 27 ; Elements, 45. Gage's 
Introduction, 24 ; Elements, 28. Hall and Bergen, 10, 11, 14-16. 

Exercise 11. — Owing to the amount of mercury required, the 
author alternates this exercise with Exercises 9 and 10, so that 
but four sets of apparatus are used for a section. Examples, 
where V = 1 : 1.10 : : 1.31 : 1.71 ; P = 1 : 1.14 : : 1.30 : 1.72. 

References. Avery's Principles, 179 ; Elements, 45, 282-287. 
Gage's Introduction, 28, 37-39 ; Elements, 50. 

LIGHT. 

Exercise 1.— Example : average of five trials, 1/AL + 1/LS / 
= 0.05637 1/F = .055. 

References. Avery's Principles, 420-425, 442-459, 472-481, 
427 ; Elements, 579-584, 588, 611-633, 656-666. Gage's Intro- 
duction, 260-267, 278-292, 317-321 ; Elements, 300-308, 315-333, 
362-367. Hall and Bergen, 230-232, 249, 261-263, 265, 266, 
272-278, 279-285. 



272 APPENDIX B. 

Exercise 3. — Chief error in getting exact area. Fair results : 
example ratios of distances, 1 : 1.36 : 2.22 : 2.55. Ratios of areas 
were 1 : 1.4 : 2.0 : 2.5. 

References. Avery's Principles, 426, 428 ; Elements, 585-587, 
589. Gage's Introduction, 268, 269 ; Elements, 309-314. Hall 
and Bergen, 234-236. 

Exercises 2 and 4. — In Exercise 2 the chief error lies in the 
fact that different candles seldom give flames of equal intensity. 
Example of results, candles 1:2:4: distances were 1 : 1.78 : 2.3. 
A determination by the author where care was used to get 
similar flames, gave : candles 1:2:3. Distances 1 : 1.8 : 3.1. 

References. Gage's Introduction, 270-272. Hall and Bergen, 
239, 240. 

SOUND. 

Exercise 1.— References. Avery's Principles, 328-332, 338, 
339, 346-352; Elements, 428-437, 443-447, 454-471. Gage's 
Introduction, 242-259 ; Elements, 276- 299. Hall and Bergen, 
212-217, 220, 221, 223-225, 228, 229. 

Exercise 2. — A still simpler method would be to measure the 
time elapsing between seeing the smoke and hearing the report 
of a gun about half a mile from the observer. Example : At 
15.5°, Air, 325 m., Carbon dioxide, 283 m. per second ; fork used 
= 528. Velocity of sound at 0, 333 m. per second. Add .6 m. 
per degree centigrade. 

References. Avery's Principles, 317-321, 325, 326, 330, 333, 
340-345; Elements, 415-427, 440, 441, 442, 448-453. Gage's 
Introduction, 216-241 ; Elements, 247-275. Hall and Bergen, 
199-207, 211. 



INDEX. 



%W* Numbers above 204 refer to teachers' edition. 



Abbreviations, metric, 59 

Absorption and radiation, 150; 
exp. 151; app. 218; notes and 
ref. 268 

Action of acid on bodies, exp. 
17; attracted body on magnet, 
4; exp. 5; notes and ref. 256; 
currents on magnets, exp. 25; 
notes and ref. 257; force, exp. 
153; app. 220, 247; notes and 
ref. 269; magnet free to move, 
exp. 5 

Action and reaction, 6; exp. 178, 
179; app. 177. 180, 220, 249; 
notes and ref. 271 

Ampere's law, 27; exp. on, 25 

Angular forces, composition and 
resolution of, 160 

Apparatus, 6, 207; construction 
of: density and specific gravity 
242; dynamics, 247; electricity 
225; heat, 244; light, 252 
magnetism, 224; mensuration 
237; sound, 254; lists of: den 
sity and specific gravity, 217 
dynamics, 220; electricity, 214 
heat, 218; light, 222; magnet 
ism, 214; mensuration, 216 
sound, 222 

Archimedes' principle, exp. 93 
notes and ref. 261 

Atmospheric pressure, exp. 107; 
app. 217, 243; notes and ref. 
263. 



Balance, 79, 217, 238, 239; 

spring, 82, 85, 217, 219, 220; 

substitute for, 247 
Battery, 30; fluid. 215, 227 
Binding-posts, 223; substitute, 

230; English, 231 
Boiling-point, exp. 126; notes 

and ref. 267 
Boyle's law, 185; exp. 186; app. 

185, 220, 250; notes and ref. 

271; calibration of tube, 251 
Breaking circuit, 29; magnets, 

exp. 8; notes and ref. 256 
Bunsen burner, 112, 218; pho- 
tometer, 194 
Burette, 71, 216; substitute, 237 

Calibration of a tube, 146, 251 
Calorie, 129 
Calorimeter, 130, 218 
Candle-power, 199; exp. 200; 

app. 199, 222, 254 
Cell: see Galvanic Cell. 
Cells, methods of connecting, 

exp. 36; notes and ref. 258 
Centre of gravity, of pendulum, 

175 
Changing systems of units, 58 
Chemical change, exp. 87; notes 

and ref. 261; thermometer, 

117, 218 
Circuit, 24; introducing into, 29 
Coefficient of cubical expansion, 

139; gas, exp. 146; app. 218, 
273 



274 



INDEX. 



244; notes and ref. 261; liquid, 
exp. 145; app. 218, 245; notes 
and ref. 261; linear expansion, 
138; exp. 140, 141; «pp. 139, 
142, 218, 246; notes and ref. 
268 

Coils of wire, 32, 214, 232 

Components, 160; of angular 
forces, 160; parallel forces, 
166 

Compass, 6, 7; substitute, 214, 
224 

Composition of angular forces, 
160; exp. 162; app. 220, 247; 
notes and ref. 270; parallel 
forces, exp. 166; app. 220, 248; 
notes and ref. 270 

Conductors, 24; in series or par- 
allel, 33 

Conduction of heat, 116 

Conjugate focal length, 193 

Constant errors, 85 

Conditions affecting electrical 
resistance, 29; exp. 30; app. 32, 
214, 232; notes and ref. 257; 
pitch, exp. 201; app. 201, 222, 
254; notes and ref. 272 

Connector, 215 

Convection, 116 

Cost of equipment, 207 

Counterpoising, 82 

Cross-section of tube, exp. 76; 
app. 216; notes and ref. 260 

Current, electric, 20, 24; revers- 
er, 225 

Currents, induced, 52; exp. 53; 
app. 52, 214; notes and ref. 259 

Curve plotting, 122, 124 

Density, 89; unit of, 91; exp. 90; 
app. 217; notes and ref. 261; 
and specific gravity, app. con- 
struction, 242; lists, 217; notes 
and ref 261 

Determination of length, 59, 62; 
volume, 67; diameter of a 
sphere, 61 

Diagrams, 21 

Direction of current, 24 

Distance and intensity of light, 
194; exp. 195; app. 195, 220. 
252; notes and ref. 272 



Distribution of heat in a rod, 
exp. 114; of magnetism, 2 

Dynamics, Exercise 1, 153; notes 
and ref. 269; construction, 
247; list of, 220 

Dynamo, 54; model, 233 

Dynamometer,83; substitute,247 

Edison current, 208; uses of, 210 

Elasticity, force of, 183; of a gas, 
186 (see Boyle's law); of a 
solid, exp. 184; app. 183, 220, 
252; notes and ref. 271; spe- 
cific gravity by exp. 190; app. 
190, 220, 252 

Electricity, 17; construction,225; 
lists of, 214 

Electro-magnetism, exp. 50; app. 
214; notes and ref. 259 

Electro-motive force, 49; exp. 48; 
app. 214; notes and ref. 259; 
standard, 49 

Electric current, 20; circuit, 29 

Electrical resistance, 33; exp. 34; 
notes and ref. 258; conditions 
affectiner exp. 29; relative, 40 

Elements of cell, 23 

English units, 57; measure, 57 

Equilibrium, 156 

Equipment, cost of, 207; gen- 
eral, 223 

Errors, 85 

Essays, 206 

Exciting fluid, 23 

Expansion, suggestions for illus- 
trating, 265; "coefficients of, 139 

Field of magnet, 12 

Float, 72 

Focal length of lenses, 191 

Focii of lenses, exp. 191; app. 
191, 222, 252; notes and ref. 271 

Focus of lens, 191 

Force, 4, 269; action on a body, 
153; composition of, 160; exp. 
162, 166; notes and ref. 270; 
form of lines of, 15; graphical 
representation of, 158; measure- 
ment of, 157; of elasticity, in 
a solid, 183; exp. 184; notes and 
ref. 271; in a gas, exp. 186; 
notes and ref. 271; of friction, 



INDEX. 



275 



156; exp. 156; app. 220, 247; 
notes and ref. 269; of tenacity, 
exp. 181; notes and ref . 271 

Forces, direction indicated by 
signs, 159; geometrical addi- 
tion and subtraction of, 159; 
by algebra, 159; parallelogram 
of, 163; exp. 164; parallel, 
composition of, 166 

Formula for changing system of 
linear units, 58, 186; cubical 
coefficient of a gas, 150; den- 
sity, 90; diameter of circle 
from area, 78; heat quantity, 
129; latent heat, 136, 137; lin- 
ear coefficient of expansion, 141, 
144; number grms. in an oz., 
83; number ins. in a meter, 63; 
specific gravity by elasticity, 
190; by moments, 189; of li- 
quids, 93; by balancing, 104, 
106, 109; of solids, 97, 98; 
specific heat, 132, 133; work 
(inclined plane), 172 

French units, 57 

Friction, force of, 156 

Galvanic cell, 23; diagram of, 
24; direction of current in, 24; 
construction of, 214, 227, 236 

Galvanometer, 27; construction 
of, 215, 229; diagram of, 28; 
precautions, 28; sensitive, 215, 
231 

Gas, temporary piping, 211 

Gases, elasticity of (see Boyle's 
law), 185 

General laboratory equipment, 
211, 223; method, 34, 205; sug- 
gestions, 205, Preface; study of 
a magnet, exp. 1; app. 214; 
notes and ref. 256 

Glass cutting, 208 

Graduated cylinder, 67: use, 70; 
flask, 72 

Graphical representation o f 
forces, 158; of results, 122 

Heat, app. 218; construction, 244; 
notes and ref. 264; capacity, 
127, exp. 127; app. 218, notes 
and ref. 269; conduction of, 



116; how it travels, exp. 113; 
app. 113, 218; notes and ref. 
265; radiation of, 116; specific, 
128 
Heating, precautions in, 113 

Induction, 6 

Induced magnetism, exp. 8; notes 

and ref. 256; currents, exp. 52; 

app. 216; notes and ref. 259 
Inducing magnet, 10 
Inclined plane, 169; exp. 170; 

app. 170, 220, 248; notes and ref. 

270; as wedge and screw, 173 
Intensity of light, 194 
Irregular body, volume of, exp. 

74 

Laboratory work, preparation of, 
207, Preface; equipment, 223 

Latent heat, 133; exp. 134, 137; 
app. 134, 219, 224; notes and 
ref. 267 

Law, 6; of cooling, exp. 124; 
notes and ref. 266; of induced 
poles, exp. 8; magnets, 10; notes 
and ref. 256; of magnet, 6 

Lectures, 206 

Length, determination of, 59; 
units of, 56; of pendulum, 175; 
units of, 57 

Lenses, focal length, 193; conju- 
gate, 193 

Light, app. construction, 252; 
list, 222; notes and ref. 271; in- 
tensity of, 194; effect of distance 
on, exp. 195; app. 195, 222, 
253; notes and ref . 272; radia- 
tion of, 197; exp. 197; app. 
222, 253; notes and ref. 272; 
unit of, 199; exp, 200; app. 199, 
252, 254; notes and ref. 272 

Lines of magnetic force, 12; exp. 
13; app. 214; notes and ref. 256 

Linear measurements, 57; scales, 
English, 59; French, 59; read- 
ing, 60; pracitce in use of, exp. 

. 63 . 
Liquid pressure due to weight, 

99; exp. 100; app. 217, 242; 

notes and ref. 262; weighing, 

81 



276 



INDEX. 



Machines, 169 

Magnet, general study of, exp. 1; 

bar, 2; action of attracted body 

on, exp. 4; of currents on, exp. 

25; notes and ref. 257 
Magnets, breaking, exp. 8; notes 

and ref. 256; law of, induced, 

exp. 10; notes and ref. 256; 

mutual action of two, exp. 6; 

notes and ref. 256 
Magnetism, app. 224; lists, 214; 

induced, exp. 8; notes and ref. 

256 
Magnetic force, Hues of, exp. 12; 

field, 12; poles, 6 
Measurement, of forces, 157; of 

resistance, exp. 42, 45; app. 

226; notes and ref. 258; notes 

on, 56 
Measuring vessels, 67, 71, 72; 

substitutes, 237 
Melting point, exp. 125; notes and 

ref. 267; tubes, 125 
Meniscus, 68 
Mensuration, app. 237; notes and 

ref. 260; list, 216 
Mercury, 214, 218, 220; care of, 

210: calibration by, 237, 251; 

cups, 214, 230 
Meter, 57; sticks, 216 
Metric system, 57; abbreviations, 

59; units, 57; values, estima- 
tion of, exp. 84; notes and ref. 

261; weights, 79 
Moment of a force, 169; specific 

gravity by, exp. 189 
Motor, principle, exp. 54; model, 

233 
Multiple arc, 33 

Naming of poles, 6 
Notes, form of, 205; on errors, 
85; on measurement, 56 

Ohm,39 

Parallel forces, exp. 166 

Pendulum, exp. 174; app. 174, 
220; notes and ref. 270 

Personal errors, 85 

Phenomenon, 2 

Photometer, liunsen, 194; Rum- 
ford, 199 



Physical and chemical change, 
exp. 86; notes and ref. 261; app. 
216 

Plates, positive and negative, 24 

Polarity, 3, 4 

Poles, 4; naming, 6; action of one 
on another, 6; induced, exp. 
8; law of, exp. 10 

Practice in determining volume, 
exp. 62; app. 216; notes and ref. 
260; estimating metric values 
exp. 84; notes and ref. 261; use 
of linear scales, exp. 62; app. 
216; notes and ref. 260; weigh- 
ing, exp. 83; app. 216; notes 
and ref. 261 

Qualitative experiment, 4 
Quantitative experiment, 4 

Rack with wires, 41, 215, 231 

Radiation of heat, 116; and ab- 
sorption, 150; exp. 151; app. 
218; notes and ref. 268; of light, 
197; exp. 197; app. 222, 253; 
notes and ref. 272 

Ratio, 89 

Reading by reversal, 29; linear 
scales, 61; pointer against 
scale, 62; volumes, 68 

Relation of circumference to di- 
ameter, exp. 64; app. 216; notes 
and ref. 260 

Relative resistance, exp. 40; app. 
41, 215, 231; notes and ref. 258 

Residual magnetism, 10 

Resistance, 40; unit of, 39; con- 
ditions affecting, 29, 33; meas- 
urement of, exp. 42, 45; box, 
39, 40, 215, 225 

Retentivity of steel, 10 

Resultant, 160; of forces, exps. 
162, 166 

Reverser, 215, 225 

Rheostat, 39, 208 

Scales, linear, 57; balances, 79, 
217; substitutes; 239; of spring 
balances, 82 

Sections, size of, 208 

Solution, exp. 152; notes and ref. 



INDEX. 



211 



Sound; app. 254; list, 222; notes 
andref. 272; pitch of, exp. 201; 
velocity of, exp. 203 

Special method, 34, 205; con- 
dition of wire, 20 

Specific gravity, of a liquid, by 
bottle, 92; exp. 92; app. 217; 
notes and ref. 261; balancing, 
103; exp. 104; app. 205, 217, 
243; notes and ref. 263; atmos- 
pheric tension, 109; exp. 109; 
app. 110, 217, 243; notes and 
ref. 264; by floating body, exp. 
107; app. 217; notes and ref. 
263; of solids, 96; exp. 96; app. 
217; notes and ref. 262; bottle : 
92, 94, 217; without scales or 
weights, exp. 189; app. 220. 
252; notes and ref. 271 

Specific heat, 128, 129; exp. 130: 
app. 218 ; notes and ref. 267 

Spring balance, 82, 217, 220; 
error, 85; substitute, 247 

Square measure, 58 

Sulphate of copper cell, 236, 259 

Substitutes, balances, 239; bind- 
ing post, 230; compasses, 224: 
dynamometer, 247; measuring 
vessels, 237; weights, 241 

Support, for apparatus, 251 

Surface measure, 58 

T square, 171, 220 
Temperature, 116; and physical 

form, 119; exp. 120; app. 119, 

218; notes and ref. 266 
Tenacity, exp. 181 
Testing thermometers, exp. 118; 

app. 218, 244; notes and ref. 

265 
Thermometers, 117, 218, 244; 

exps. 266 



Tumbler cell, 23, 215, 237 
True focal length, 193 

Unit of force, 158; of length, 57; 

of surface, 58; of volume, 58; 

of measure, 56; English, 57; 

French, 57; change from one 

system to another, 57; theory 

of, 56. 
Useful books, 212 

Velocity of sound, exp. 203; app. 
222; notes and ref. 272 

Vibration of pendulum, exp. 174; 
wires, exp. 201 

Voltaic electricity, 17; produc- 
tion, exp. 18; notes and ref. 
257 

Volume, units, 58; scales, 67, 71; 
practice in determination of, 74 

Weighing, proper method of, 80; 
of liquids, 81; solid in liquid, 
95; by counterpoising, 82 

Weight, units of, 78; determina- 
tion of, 78; by spring balance, 
82; in chemical and physical 
change, 86; liquid pressure due 
to, exp. 99; apparatus for, 99, 
217, 242; of liquid displaced by 
floating body, exp. on 10Q\app. 
217; notes and ref. 260; lost by 
a body immersed in a liquid, 
93; exp. 94; notes and ref. 261 

Weights, 79, 217, 241 

Wheatstone's bridge, measure- 
ment of resistance by, 45; app. 
215, 225; 

Wire, 223; coils of 214, 232; 
rack with, 214, 231 

Zinc, amalgamated, 18 




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